WEBVTT
Kind: captions
Language: en
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we got wolfstock in two weeks
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thats a lot of fun for those of you who are freshman
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the homecoming is a lot of fun
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we have midterm three weeks from tomorrow
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you just had a midterm
00:00:21.640 --> 00:00:26.680
youll have chemistry somewhere in the middle and if your lucky also biology
00:00:28.700 --> 00:00:33.100
or math, if your really lucky all your finals will be on the same day
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that happens
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alright
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first lets review our rules of it
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so this should be review for everyone
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okay
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if had x to the 5
00:01:12.260 --> 00:01:13.140
plus x to the 8
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what can i do with the powers?
00:01:20.280 --> 00:01:22.440
if i add them i would get x to the 13
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i get nothing
00:01:25.320 --> 00:01:29.000
if you add two things like that you cant do anything to it
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you can factor out the x to the 5, but you cant do anything if youre just adding the 2
00:01:33.240 --> 00:01:35.620
if you are multiply them
00:01:35.840 --> 00:01:37.280
you can add the powers
00:01:41.680 --> 00:01:43.440
do you know why thats true?
00:01:44.060 --> 00:01:46.940
that is true because x to the 5
00:01:47.600 --> 00:01:49.300
is x times x times X
00:01:49.720 --> 00:01:50.680
times x times x
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the x to the 8 is x times x
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x 8 times
00:01:58.640 --> 00:02:00.780
so when you put it together you have 13 x
00:02:01.560 --> 00:02:07.420
thats why x to the 5 times x to the 8, you get x to the 13
00:02:08.120 --> 00:02:12.360
if you have x to the 5 plus x to the 8, its just x to the 5 plus x to the 8
00:02:13.220 --> 00:02:14.820
if i raise it to the power
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then im getting
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x to the fifth times x to the fifth times x to the fifth
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eight times
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so thats x to the fifth times 8
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which is to the fourty
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so you want to make sure you dont confuse these 3
00:02:37.720 --> 00:02:38.220
things
00:02:43.740 --> 00:02:44.860
the general rule
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you have x to the a
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times x to the b
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thats gonna equal x to the a plus b, it switched up when we logarithms
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got x to the a
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raised to the b
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thats x to the a
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b
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what if i had x to the a over
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x to the a divided by x to the b
00:03:17.880 --> 00:03:21.240
so thats gonna be x to the a minus b, why is that true?
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suppose we had x to the 8 over x to the 5
00:03:31.280 --> 00:03:33.680
so whats going on on top? we have 8x's
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good thing i didnt pick a big number
00:03:41.220 --> 00:03:43.140
and on the bottom we have 5x's
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so i can cancel those
00:03:52.920 --> 00:03:55.160
1,2,3,4,5
00:03:55.780 --> 00:03:56.740
and left with 3
00:03:56.740 --> 00:03:58.600
so thats why you have to do the subtraction
00:03:58.760 --> 00:04:00.760
you have x to the 8 over x to the 5
00:04:01.320 --> 00:04:02.200
so in general
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we gotta make sure, we remember these rules
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and you will read those
00:04:10.560 --> 00:04:15.440
so we have some stuff that has exponents and it could be very tricky but you make sure you know your exponent rule
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this shows up alot in first semester calc
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do you a lot of playing around with exponents
00:04:24.900 --> 00:04:25.860
so far so good?
00:04:32.140 --> 00:04:33.660
alright what if i have?
00:04:46.260 --> 00:04:48.080
what if i have x to the 5
00:04:48.540 --> 00:04:50.240
over x to the 5
00:04:50.780 --> 00:04:52.540
well that would just be one
00:04:53.460 --> 00:04:54.980
so what do i do with those powers
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well we get 5 minus 5 which equals 0
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if you think about it more genrally
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if i have x to the a
00:05:05.780 --> 00:05:07.180
over x to thea
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thats x to the a minus a
00:05:11.600 --> 00:05:12.960
which is x to the zero
00:05:14.420 --> 00:05:16.020
which is 1. so therefore
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any x raised to the 1 is 0, unless x is zero
00:05:21.340 --> 00:05:22.020
which dont worry about that
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make sense so far?
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you can add that
00:05:28.580 --> 00:05:29.860
to our list of rules
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you have a couple more coming
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so far so good?
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what about if we have 1 over
00:05:53.880 --> 00:05:54.680
or negative
00:05:54.680 --> 00:05:56.500
what about a negative power
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what does x to the minus a equal
00:06:07.840 --> 00:06:10.720
correct. nobody heared that but thats okay
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that would be the same as x to the zero minus a
00:06:17.680 --> 00:06:23.520
which is like saying x to the 0 over x to the a, given in the other direction
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if you have x to the 0 over a is like x to the 0 minus a
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you zwitch x and negative a, since x to the 0 is 1
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thats 1 over x to the a
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si another rule for us
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what about
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okay what about x to the 1/a
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you know what that one is?
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perfect thats the a root
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technically 1/2, the square root x to the 1/3. cubed root
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you go all the way back and stop
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so far so good?
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with those
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it would be rules of exponent
00:08:06.640 --> 00:08:10.000
sure that will go up later, i dont have my glasses on
00:08:12.420 --> 00:08:19.940
one of the things we want to make sure is the rules of exponents because this is precalculus and here you already know the rules of exponents
00:08:20.480 --> 00:08:22.720
anyone do the 10th webassign yet?
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was webassign due? okay its done good
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howd we do on it?
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badly? well..
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well yea ill talk to professor sutherland, its out of 14 it should be out of 12
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thats okay we will recover
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oh good, okay alright
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so alright back to what we were talking about the other day
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remember we talked about circles
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i didnt do anything on ellipses
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so an elipse is sort of a stretched out circle
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its a circle where instead of the
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then being round its more like that
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the elipse has
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two axis like that so sort of two diameters
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it has a long diameter and a short diameter
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so this is called the major axis
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and this is called the minor axis
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why is ellipse important, well conterie orbits all ellipses
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in case you were wondering
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people spends thousands of years trying to get conterie orbits to work on circles
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and along came Kepler and said or you can just do ellipses
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and that solved the problem
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made a lot of people feel really dumb
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thats where keplers law came from, when you take astronomy
00:10:19.140 --> 00:10:22.120
you learn that and then after that things a lot easier
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not exactly an ellipse but much much muchh closer
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so its pretty close to a circle
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but the earths orbit is a little bit wider then it is
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this is wider in this direction than in that direction
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well that sounds like a lot but
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whats the circumference of the earths core?
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no
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so its 93 miles from here to the sun, you got to multiply that by 2pi
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so 150 millione
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its a little more in one direction then the other
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so thats the major x and the minor x, so what the equivalent of the radius
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is the semi major axis
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and the semi minor axis
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call that a and call that b
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no
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we originally had x squared plus y squared equals r squared
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now what happens is
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you think thats a circle right?
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circle
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if you divide it by r squared you get this
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little struggle with those twos
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its goes back to the twos probably
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not that long
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so thats another way to think of a circle, notice these are the same radi
00:11:55.560 --> 00:11:56.820
where an ellipse
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you get x squared
00:11:59.420 --> 00:12:00.380
over a squared
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plus y squared
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over b squared
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and of course we can just the way we shift a circle
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we could..if i had center h,k
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a more adavnce version
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all im gonna show you about ellipses
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no need to do more
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theres a lot to learn about ellipses but its not really our focus of course
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gonna erase this
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so for example
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suppose i gave you
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gave something like that
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we want to just graph it
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so first we climb the center. the center is the 2
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comma negative 1
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so you go to 2
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and you go down 1
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and thats where the center is
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and its very simple whats the square root of 16
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4
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you move 4 in the x direction
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and 4 in each direction
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and the square root of 9 is 3 so you go to
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3 in this direction
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3 in this direction
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your ellipse
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not very hard. so this distance is 4
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and this is 4. this because the square root of 6
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the distance is 3
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3
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in the center is a 2,-1
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not hard right?
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thats all im gonna ask of you of ellipse, im asking you to graph it not asking for completing the graph, whats the equation
00:14:44.820 --> 00:14:46.820
okay so im just working in the other direction
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we good with these?
00:14:53.120 --> 00:14:56.560
so i want to make sure we got the concept of parabulas
00:14:56.560 --> 00:14:57.560
you just did the vertex
00:14:57.560 --> 00:14:59.740
roots and completing the square thing
00:15:00.660 --> 00:15:01.620
we did circles
00:15:02.840 --> 00:15:03.480
ellipses
00:15:04.060 --> 00:15:04.560
lines
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now we are gonna do a whole new different kind of function
00:15:09.320 --> 00:15:13.800
you guys might finish early today, unless you guys want to say to 6:50
00:15:14.120 --> 00:15:16.680
some of you complained about that once
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you want me to tak eit
00:15:50.380 --> 00:15:51.740
the negative one,
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that comes from here
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so the center
00:15:56.120 --> 00:15:56.620
is
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x minus 2 and y plus 1 gives you the center positive 2 and negative 1
00:16:02.800 --> 00:16:05.040
because you said x minus 2 equals 0
00:16:05.280 --> 00:16:08.240
you set y plus 1 equal to 0 and thats the center
00:16:08.280 --> 00:16:10.200
and then the square root of 16
00:16:11.960 --> 00:16:14.040
equals a and the square root of 9
00:16:15.180 --> 00:16:15.680
equal b
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and remember its x minus h
00:16:22.280 --> 00:16:23.800
squared over a squared
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plus y minus k
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squared over b squared
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equal 1
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and this is an ellipse
00:16:36.260 --> 00:16:37.780
has a centricity of 4/3
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how do we know if the ellipse is tilted the other way?
00:16:45.460 --> 00:16:47.540
this isde is greater than this?
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can i pull this down?
00:16:51.500 --> 00:16:52.000
one hand
00:17:04.820 --> 00:17:05.940
what if i did that
00:17:07.200 --> 00:17:08.720
so its very smilar to the other one
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except i switched the 9 and 16
00:17:18.860 --> 00:17:20.380
now what happens? well
00:17:22.580 --> 00:17:25.220
i have the center still at negative 2 one
00:17:30.540 --> 00:17:32.900
and a is the square root of 9
00:17:34.380 --> 00:17:35.980
b is the square root of 16
00:17:42.280 --> 00:17:43.860
i go to 2,-1 again
00:17:44.620 --> 00:17:46.780
this time i go 4 in the y direction
00:17:49.140 --> 00:17:50.340
that looks about 4
00:17:53.220 --> 00:17:54.980
and i go 3 in the x direction
00:17:58.500 --> 00:18:00.180
and it will look like that
00:18:02.000 --> 00:18:05.360
thats when you can tell if its a long skinny ellipse
00:18:05.700 --> 00:18:07.220
or a short wide ellipse
00:18:07.340 --> 00:18:08.540
not sure to say fat
00:18:12.560 --> 00:18:14.480
because we dont use that word
00:18:20.660 --> 00:18:21.540
how we doing?
00:18:22.280 --> 00:18:24.120
what are we confused about?
00:18:35.280 --> 00:18:37.200
okay 3 spaces from the center
00:18:37.760 --> 00:18:41.500
okay we need to move 3 in the x direction
00:18:42.420 --> 00:18:43.940
and 4 in the y direction
00:18:44.900 --> 00:18:47.000
from the the center root 2,-1
00:18:51.760 --> 00:18:52.260
okay?
00:18:56.320 --> 00:18:59.440
none of this will be in the part one of the retake
00:19:00.560 --> 00:19:01.060
okay
00:19:04.680 --> 00:19:07.040
study the exam you get back
00:19:07.040 --> 00:19:13.220
and look back at the webassigns. the new version of the part 1 could look a lot like the old version
00:19:13.220 --> 00:19:15.820
if its the same kind of question, gott do it again
00:19:16.280 --> 00:19:19.160
again. maybe 50 times
00:19:19.600 --> 00:19:20.660
or once
00:19:23.760 --> 00:19:26.000
you dont have too, im happy for you
00:19:29.720 --> 00:19:31.800
everybody ready to erase this?
00:19:31.800 --> 00:19:33.100
who needs another minute?
00:19:50.500 --> 00:19:53.060
alright something totally different
00:19:55.860 --> 00:19:59.860
how many of you ever did polynomial division in high school?
00:20:01.400 --> 00:20:05.740
or synthetic division? oh yes that. you love that stuff
00:20:06.360 --> 00:20:07.480
love that stuff okay?
00:20:08.380 --> 00:20:12.220
polynomial long division is a tool youll need in calculus
00:21:07.500 --> 00:21:08.060
suppose
00:21:09.020 --> 00:21:12.800
i have no idea why but suppose i take this polynomial
00:21:13.340 --> 00:21:14.860
and divide it by x plus 1
00:21:15.520 --> 00:21:17.600
or another words, i want to know
00:21:17.980 --> 00:21:19.260
if this polynomial
00:21:19.800 --> 00:21:21.080
can equal to x plus 1
00:21:22.180 --> 00:21:24.100
times some other polynomial
00:21:25.840 --> 00:21:28.000
because if it is, we know it has a 0
00:21:28.020 --> 00:21:29.400
at x equals -1
00:21:29.400 --> 00:21:31.680
this polynomial of course would be a quadratic
00:21:32.420 --> 00:21:35.560
because a quadratic times the x plus 1 would give you something cubed
00:21:37.180 --> 00:21:41.100
so lets figure out what the quadratic is, how would i do that
00:21:41.100 --> 00:21:44.400
i would do that with something called polynomial long division
00:21:48.260 --> 00:21:49.220
you write this
00:21:49.860 --> 00:21:52.340
thats the way you wrote long division
00:21:52.780 --> 00:21:54.380
back in the second grade
00:21:55.840 --> 00:21:56.640
thirdgrade
00:21:57.040 --> 00:21:58.620
any grade
00:21:58.620 --> 00:22:02.900
whatever grade you learned it in. i dont remember when i learned it in
00:22:04.340 --> 00:22:05.940
i think around 3rd grade
00:22:05.960 --> 00:22:07.480
does that sound right?
00:22:08.420 --> 00:22:09.860
2nd grade, 3rd grade?
00:22:10.320 --> 00:22:11.680
it was a long time ago
00:22:13.920 --> 00:22:14.500
thank you
00:22:15.620 --> 00:22:16.120
but it was
00:22:17.060 --> 00:22:18.360
trying to think when i
00:22:19.180 --> 00:22:20.500
2nd grade would of been
00:22:23.060 --> 00:22:23.940
ten years ago
00:22:26.400 --> 00:22:28.300
no am i that old?
00:22:31.200 --> 00:22:34.320
9, 9 that means i graduate high school next year
00:22:40.720 --> 00:22:43.700
so no matter how you do division oka
00:22:43.700 --> 00:22:47.720
you take division you divide this into each term
00:22:47.860 --> 00:22:52.580
you can bring it down multiple and pull it down and factor and do it again
00:22:53.680 --> 00:22:57.040
so what you do is you only look at the 1st term x
00:22:57.040 --> 00:23:00.140
and you say to yourself how many times does x go into x cubed
00:23:00.140 --> 00:23:01.760
well another way to think about it is
00:23:01.760 --> 00:23:03.940
x times what gives you x cubed
00:23:04.180 --> 00:23:05.680
x times x squared
00:23:06.160 --> 00:23:07.280
gives you x cubed
00:23:09.580 --> 00:23:12.060
so x goes into x cubed, x squared times
00:23:12.060 --> 00:23:14.720
and the same way you did the division, you take the x squared
00:23:14.720 --> 00:23:16.400
and you multiply it by this
00:23:16.740 --> 00:23:20.160
and you get x cubed plus x squared
00:23:23.580 --> 00:23:27.260
okay then what do you do with the division, you subtract
00:23:29.400 --> 00:23:31.000
x cubed minus x cubed is 0
00:23:31.700 --> 00:23:34.340
5x squared minus x squared is 4x squared
00:23:37.220 --> 00:23:38.580
and bring down the 7x
00:23:39.440 --> 00:23:41.280
just the way you do division
00:23:42.460 --> 00:23:44.500
so what did i do.. i said x
00:23:44.760 --> 00:23:46.120
has to go into x cubed
00:23:46.120 --> 00:23:48.960
how many times, it has to go in x squared times
00:23:49.120 --> 00:23:52.740
x squared times this gives you x cubed
00:23:52.740 --> 00:23:55.040
so now i took x squared and multiplied it by the whole number
00:23:55.540 --> 00:23:58.180
i get x cubed plus 1 x cubed from x squared
00:23:59.360 --> 00:24:00.320
and i subtract
00:24:02.760 --> 00:24:03.640
so i subtract
00:24:03.640 --> 00:24:05.300
x cubed minus x cubed goes away
00:24:05.940 --> 00:24:07.860
5x squared goes to 4x squared
00:24:08.040 --> 00:24:10.120
and you bring down the next term
00:24:10.660 --> 00:24:11.860
and you do it again
00:24:11.860 --> 00:24:15.280
x times what gives you 4x squared, 4 x
00:24:18.280 --> 00:24:20.480
but 4x times x is 4x squared
00:24:21.900 --> 00:24:22.540
4x times 1
00:24:24.440 --> 00:24:24.940
is 4x
00:24:27.820 --> 00:24:28.780
and i subtract
00:24:30.620 --> 00:24:32.780
4x squared minus 4x squared is 0\
00:24:33.480 --> 00:24:35.240
7x minus 4x is 3x
00:24:36.920 --> 00:24:38.860
bring down the 3
00:24:43.020 --> 00:24:47.260
now x goes into 3x how many times? it goes in 3 times
00:24:49.740 --> 00:24:50.940
so this gives me 3x
00:24:52.000 --> 00:24:52.920
plus 3
00:24:53.520 --> 00:24:54.800
and when i subtract
00:24:55.480 --> 00:24:57.420
i get 0 which means it goes in perfectly
00:25:00.180 --> 00:25:02.020
so you can use this to factor
00:25:02.420 --> 00:25:03.300
polynomials
00:25:03.620 --> 00:25:06.100
cause now i can look at this polynmial
00:25:09.520 --> 00:25:14.160
never done this before? well we will do a couple of these to get the idea
00:25:14.840 --> 00:25:16.360
im gonna pull this down
00:25:23.560 --> 00:25:25.640
okay by the way this is accurate
00:25:34.840 --> 00:25:41.640
why would this be useful? well go back to the original polynomial, x cubed plus 5x squared plus 7x plus 3
00:25:41.700 --> 00:25:45.280
i now know that this has a 0x equals negative 1
00:25:45.780 --> 00:25:47.700
a second 0 x equals negative 1
00:25:47.760 --> 00:25:49.180
so two of them
00:25:49.660 --> 00:25:51.340
and a 0x equals negative 3
00:25:51.340 --> 00:25:54.060
i can graph it and do all sorts of fun stuff from there
00:25:54.320 --> 00:25:54.820
or not
00:25:56.180 --> 00:25:59.300
i vote for not but theres lots of stuff you can do
00:26:00.020 --> 00:26:01.700
try another one of these?
00:26:02.480 --> 00:26:02.980
sure
00:26:39.740 --> 00:26:41.960
rote these down and left them in the office
00:26:42.800 --> 00:26:44.400
suppose i wanted to know
00:26:50.580 --> 00:26:52.900
i want to know if this factorable by
00:26:54.120 --> 00:26:55.120
x plus 2
00:26:58.540 --> 00:27:01.820
im gonna to this one and then ill let you guys do one
00:27:04.480 --> 00:27:06.080
so i write this as x plus 2
00:27:08.280 --> 00:27:08.920
goes in to
00:27:09.820 --> 00:27:18.480
x cubed -3x squared minus 8x plus 4
00:27:30.340 --> 00:27:33.920
so im gonna take x and divide it into x cubed
00:27:34.780 --> 00:27:37.020
x goes into x cubed x squared times
00:27:37.780 --> 00:27:40.100
because x squared times x is x cubed
00:27:40.260 --> 00:27:42.340
now i multiply x squared times x
00:27:43.920 --> 00:27:45.040
x squared times 2
00:27:47.580 --> 00:27:48.540
and i subtract
00:27:49.220 --> 00:27:50.340
always subtract
00:27:50.600 --> 00:27:52.840
and that will help you keep track the sign changes
00:27:55.320 --> 00:27:58.360
so the x squared goes away thats the whole idea
00:27:59.460 --> 00:28:03.140
and minus 3x squared minus 2x squared, minus 5x squared
00:28:05.760 --> 00:28:07.280
bringing down minus 8x
00:28:12.440 --> 00:28:13.400
and now repeat
00:28:14.400 --> 00:28:16.480
x times what is minus 5x squared
00:28:18.080 --> 00:28:18.640
minus 5x
00:28:18.680 --> 00:28:20.440
so you get minus 5x squared
00:28:22.160 --> 00:28:22.800
minus 10x
00:28:26.900 --> 00:28:27.780
and subtract
00:28:28.820 --> 00:28:30.980
minus 5x squared minus minus 5x squared
00:28:30.980 --> 00:28:32.840
is plus, goes away
00:28:33.560 --> 00:28:34.840
minus 8x plus 10x is
00:28:36.120 --> 00:28:36.620
2x
00:28:39.000 --> 00:28:40.040
bring down the 4
00:28:41.320 --> 00:28:45.560
and somebody will look at this and say x plus 2 would work, right?
00:28:45.860 --> 00:28:47.720
x goes into 2x 2 times
00:28:48.880 --> 00:28:50.540
so i get 2x plus 4
00:28:52.400 --> 00:28:53.360
and i subtract
00:28:54.460 --> 00:28:55.100
and i get 0
00:28:57.460 --> 00:28:58.500
so this tells me
00:28:59.160 --> 00:29:01.440
that x cubed minus 3x squared
00:29:02.360 --> 00:29:04.280
minus 8x plus 4
00:29:05.080 --> 00:29:07.840
equals x plus 2
00:29:08.740 --> 00:29:11.060
times x squared minus 5x
00:29:13.160 --> 00:29:13.660
plus 2
00:29:15.360 --> 00:29:15.860
yes?
00:29:19.380 --> 00:29:19.880
yea
00:29:22.740 --> 00:29:25.140
i love when you guys ask me that stuff
00:29:26.160 --> 00:29:29.040
it makes me feel so inadequate
00:29:45.600 --> 00:29:47.600
im not sure what you are saying
00:29:48.600 --> 00:29:49.240
this one?
00:29:50.400 --> 00:29:52.960
can i take x times x squared i get x cubed
00:29:53.380 --> 00:29:55.980
and x squared times 2 is 2x squared
00:29:56.200 --> 00:29:57.480
and then i subtract
00:30:00.240 --> 00:30:04.160
this is minus 3x ssquared minus 2 gives you minus 5x squared
00:30:05.320 --> 00:30:06.040
and minus 3
00:30:07.140 --> 00:30:08.780
minus 2 is minus 5
00:30:11.420 --> 00:30:14.060
lots of opportunities to mess up in a problem like this
00:30:17.440 --> 00:30:18.640
because subtract
00:30:21.420 --> 00:30:22.140
now im good
00:30:25.580 --> 00:30:27.100
back at my inadequates
00:30:30.460 --> 00:30:31.500
more questions
00:30:32.220 --> 00:30:32.860
feel free
00:30:33.380 --> 00:30:36.580
no love this, should i make one for everyone to do
00:30:36.740 --> 00:30:37.240
oh yes
00:30:39.080 --> 00:30:39.580
sure
00:30:40.300 --> 00:30:42.060
oh yea i have a bunch of thes
00:30:42.160 --> 00:30:44.080
im gonna make them harder too
00:30:54.480 --> 00:30:57.520
yea i had them in my office and i left them there
00:31:32.760 --> 00:31:33.880
that should work
00:31:55.680 --> 00:31:57.760
what do we know about practice?
00:31:58.600 --> 00:31:59.640
what do we know?
00:32:01.520 --> 00:32:03.660
be perfect, be practice
00:32:07.420 --> 00:32:08.860
go aim hire everytime
00:32:40.540 --> 00:32:42.720
that says x to the 4th
00:32:43.580 --> 00:32:44.540
minus 2x cubed
00:32:45.680 --> 00:32:46.880
minus 11x squared
00:32:47.780 --> 00:32:49.260
plus 13x plus 3
00:32:49.260 --> 00:32:52.400
now we are gonna divide it by x plus 3
00:32:53.280 --> 00:32:54.080
see how we do
00:33:03.280 --> 00:33:05.840
x plus 3 now i gave you a slighly hard one
00:33:08.120 --> 00:33:11.160
for those of you watching the camera go around
00:33:11.680 --> 00:33:12.720
go the other way
00:33:14.740 --> 00:33:16.180
so x goes into x to the 4
00:33:17.000 --> 00:33:18.340
x to the 3 times
00:33:35.000 --> 00:33:37.240
so x to the 3rd times x is x to the 4th
00:33:38.240 --> 00:33:41.360
x to the 3rd times 3 is 3x to the third
00:33:42.540 --> 00:33:43.900
and now you subtract
00:33:48.880 --> 00:33:51.700
negative 2x cubed minus 3 x cubed
00:33:52.380 --> 00:33:53.500
is minus 5x cubed
00:33:54.600 --> 00:33:55.880
now bring that down
00:34:03.040 --> 00:34:05.760
so x becomes something tha makes 5x cubed
00:34:07.080 --> 00:34:08.760
so thats minus 5x squared
00:34:11.060 --> 00:34:14.180
you do minus 5x squared times x is minus 5x cubed
00:34:15.400 --> 00:34:17.000
minus 5x squared times 3
00:34:18.340 --> 00:34:19.700
is minus 15x squared
00:34:22.620 --> 00:34:23.260
subtract
00:34:25.660 --> 00:34:26.540
these cancel
00:34:27.740 --> 00:34:30.620
minus 11x squared minus minus this is a plau
00:34:31.960 --> 00:34:33.680
4x squared
00:34:35.120 --> 00:34:36.160
bring that down
00:34:42.540 --> 00:34:45.540
x goes into 4x squared 4 times
00:34:47.660 --> 00:34:49.780
and you get 4 x squared
00:34:51.300 --> 00:34:52.440
plus 12x
00:34:54.780 --> 00:34:56.540
and cancel i mean subtract
00:34:58.100 --> 00:35:00.980
13x minus 12x is x
00:35:02.880 --> 00:35:05.200
plus 3, plus 1
00:35:05.720 --> 00:35:09.000
then you multiply 1 times x plus 3 and you et x plus 3
00:35:14.680 --> 00:35:20.380
so the answer when we said what is this divided by that?
00:35:20.720 --> 00:35:21.600
we said
00:35:22.000 --> 00:35:33.040
what is x to the 4 minus 2x cubed minus 11x squared plus 13x plus 3, divided by x-1
00:35:34.400 --> 00:35:37.520
and that was the question and this is the answer
00:35:43.220 --> 00:35:44.140
plus 3
00:35:57.260 --> 00:35:57.980
now, yes?
00:35:58.920 --> 00:36:01.320
one more, oh yea ill give you one more
00:36:02.400 --> 00:36:03.280
i got two more
00:36:09.160 --> 00:36:11.400
now what if it doesnt go in evenly?
00:36:11.400 --> 00:36:13.480
lets do one that doesnt go in evenly first
00:36:14.040 --> 00:36:16.360
takes me a few seconds to make one up
00:36:51.280 --> 00:36:52.600
alright ready?
00:36:54.660 --> 00:36:55.940
what do you mean no?
00:37:24.980 --> 00:37:26.820
whoop almost made a mistake
00:37:30.640 --> 00:37:32.380
ill just rewrite that because its easier for me
00:37:41.100 --> 00:37:41.600
okay
00:37:42.940 --> 00:37:44.140
ill give you 5 mins
00:37:45.960 --> 00:37:46.460
you ready
00:37:47.280 --> 00:37:50.280
who needs more time> are we ready?
00:37:51.540 --> 00:37:53.460
we ready? we were born ready?
00:38:03.160 --> 00:38:06.980
so x goes into x to the 4th, x cubed times
00:38:07.920 --> 00:38:09.620
x cubed times x
00:38:10.920 --> 00:38:11.800
is x to the 4th
00:38:13.360 --> 00:38:14.560
and x cubed times 5
00:38:15.140 --> 00:38:16.260
is 5x cubed
00:38:20.960 --> 00:38:22.080
and you subtract
00:38:24.420 --> 00:38:25.820
and minus 9
00:38:26.380 --> 00:38:26.880
plus 5
00:38:27.620 --> 00:38:28.860
4x cubed
00:38:30.420 --> 00:38:31.540
bring down the 23
00:38:32.660 --> 00:38:33.160
23
00:38:36.360 --> 00:38:38.760
x goes into 4x cubed, 4x squared imes
00:38:42.020 --> 00:38:44.720
4x times x is 4x cubed
00:38:46.000 --> 00:38:48.880
4x squared times minus 5 is minus 20x square
00:38:49.860 --> 00:38:51.540
woah time out
00:38:52.320 --> 00:38:56.260
yess yes yes negative 9 plus 5 minus 4
00:38:57.280 --> 00:38:58.720
i knew i was in troubke
00:38:59.180 --> 00:38:59.680
minus 4
00:39:08.000 --> 00:39:10.560
when i got the 43 i knew we had a proiblem
00:39:11.940 --> 00:39:12.820
and subtract
00:39:13.500 --> 00:39:20.500
and you get 3x squared and by the way, in your brain you say for a second these numbers look weird double check
00:39:20.780 --> 00:39:22.380
very easy to mess this up
00:39:23.740 --> 00:39:26.780
x goes into 3x squared 3x times
00:39:30.100 --> 00:39:31.300
so bring that down
00:39:39.060 --> 00:39:40.480
and you get x
00:39:41.460 --> 00:39:42.900
bring down the minus 5
00:39:42.900 --> 00:39:44.660
and thats just going to be plus 1
00:39:45.260 --> 00:39:47.180
howd we do one this one? good?
00:39:47.180 --> 00:39:50.040
alright now we give you a slightly harder one
00:40:19.380 --> 00:40:20.180
one more try
00:40:25.160 --> 00:40:27.400
x goes into x cubed x squared times
00:40:29.660 --> 00:40:31.420
x suqared times x is x cubed
00:40:32.660 --> 00:40:35.460
x squared times minus 5 is minus 5x squared
00:40:36.880 --> 00:40:37.380
so far
00:40:38.340 --> 00:40:38.840
so good
00:40:42.320 --> 00:40:43.440
minus 8x squared
00:40:44.380 --> 00:40:45.420
plus 5x squared
00:40:46.380 --> 00:40:47.500
minus 3x squared
00:40:48.600 --> 00:40:49.800
bring down that 4x
00:40:51.460 --> 00:40:52.180
and repeat
00:40:54.960 --> 00:40:58.380
x goes into minus 3x squared 3x times
00:41:04.720 --> 00:41:05.600
you subtract
00:41:06.900 --> 00:41:08.260
and you get minus 11x
00:41:10.240 --> 00:41:10.740
minus 1
00:41:12.940 --> 00:41:14.520
is that correct,we all happy with that
00:41:14.520 --> 00:41:18.700
so now x minus the 11x is minus 11 times
00:41:19.480 --> 00:41:21.880
and then you multiply and get minus x
00:41:23.160 --> 00:41:24.380
plus 55
00:41:25.220 --> 00:41:26.580
or i would like to say
00:41:27.580 --> 00:41:28.300
fifty five
00:41:30.920 --> 00:41:31.560
subtract
00:41:32.000 --> 00:41:34.520
you get minus 56 but wait a second
00:41:35.080 --> 00:41:36.280
its suppose to be 0
00:41:36.280 --> 00:41:39.700
so what do you do here to get minus 56, thats the remainder
00:41:40.460 --> 00:41:44.740
so the remainder, just the way it is in division
00:41:49.760 --> 00:41:53.820
so if you took x minus 5 and multiplied it by this
00:41:54.460 --> 00:41:55.500
you will get that
00:41:58.060 --> 00:41:59.580
so thats your left over
00:41:59.780 --> 00:42:02.020
so it doesnt always go in smoothly
00:42:02.480 --> 00:42:04.640
so sometimes you get a remainder
00:42:04.640 --> 00:42:07.680
that remainder is very useful if you want to find the limit
00:42:12.820 --> 00:42:14.260
you can write minus 56
00:42:21.160 --> 00:42:23.080
i got one more for use to solve
00:42:26.100 --> 00:42:28.580
how would the answer look? this would be the answer
00:42:33.960 --> 00:42:39.020
so its this goes into this and you get that
00:42:40.060 --> 00:42:42.140
okay so if this were a webassign
00:42:43.020 --> 00:42:47.120
thats what it would look like, when you get this on webassign youll get a couple
00:42:47.540 --> 00:42:50.260
be careful its very tricky to answer them
00:42:50.340 --> 00:42:52.420
you have to get it exactly right
00:42:56.080 --> 00:42:57.980
now we have one other type of thing we can do
00:42:57.980 --> 00:43:00.060
what if we are not dividing by something linear
00:43:03.360 --> 00:43:05.760
you guys should be pros at this by now
00:43:07.620 --> 00:43:10.300
you get up to now you use synthetic division but now
00:43:30.740 --> 00:43:31.780
how about that?
00:43:32.640 --> 00:43:36.960
same technique expect whats going in now isnt linear its squared
00:43:43.680 --> 00:43:46.620
so it gets a little messier then when i did x squared plus 5
00:43:46.900 --> 00:43:51.340
x squared goes in to x to the 5 x cubed times
00:43:53.400 --> 00:43:56.280
x cubed times x squared is x to the 5
00:43:57.020 --> 00:43:58.520
x cubed times 4
00:43:59.860 --> 00:44:01.280
is 4x cubed
00:44:08.660 --> 00:44:09.860
now when subtract
00:44:10.520 --> 00:44:11.560
you get x to the 4
00:44:13.000 --> 00:44:15.560
3x cubed minus 4 is minus x cubed
00:45:59.020 --> 00:46:03.260
now x squared times what is x to the 4th? x squared times x squared
00:46:05.020 --> 00:46:05.980
so far so good?
00:46:06.700 --> 00:46:09.660
so x squared times x squared is x to the fourth
00:46:11.240 --> 00:46:14.240
x squared times 4, plus 4x squared
00:46:16.240 --> 00:46:17.600
no when you subtract
00:46:19.220 --> 00:46:21.940
you minus x cubed comes down
00:46:24.420 --> 00:46:27.460
and 7x squared, we should of brought that down
00:46:28.500 --> 00:46:30.980
7x squared minus 4x square
00:46:33.060 --> 00:46:33.780
3x squared
00:46:34.060 --> 00:46:36.860
so maybe you shpuld bring down the minus 4x
00:46:39.000 --> 00:46:43.360
x squared times negative x will be negative x cubed
00:46:45.720 --> 00:46:47.720
and youll get negative x cubed
00:46:48.760 --> 00:46:52.360
minus x times 4 is minus 4x
00:46:54.240 --> 00:46:55.440
when you subtract
00:46:58.660 --> 00:47:01.360
you get 3x squared
00:47:02.840 --> 00:47:03.340
plus 12
00:47:05.480 --> 00:47:07.080
now we just multiply by 3
00:47:11.980 --> 00:47:14.060
anybody successfully get that
00:47:15.180 --> 00:47:16.160
some of you, yes
00:47:17.740 --> 00:47:18.620
very excited