00:01
Okay, so they give you f of x equals x to the 4th minus 16.
00:08
They want you to find f of 1, f of negative 1, and f of 2 minus square root of 3 using synthetic division.
00:20
So, when i do synthetic division, for x to the 4th, the coefficient for that is 1, we don't have an x cubed, we don't have an x squared, we don't have an x squared, we don't have an x, but we do have a constant.
00:33
And then for f of 1, we're going to put one on the outside.
00:37
So for the synthetic division, i'm going to bring down the 1.
00:40
1 times 1 is 1.
00:42
So we're going to put that here.
00:43
And then we're going to add 0 plus 1 is 1.
00:46
And then 1 times 1 is 1.
00:48
0 plus 1 is 1.
00:50
1 times 1 is 1.
00:53
0 plus 1 is 1.
00:54
1 times 1 is 1.
00:57
You get negative 15.
00:58
So when your remainder is left, that is the value for your 5%.
01:04
Function.
01:06
So f of 1 is negative 15.
01:11
If i do the same thing for my next problem, 1 -0 -0 -0 -0 -6, with negative 1, i'm going to bring down my 1.
01:24
Negative 1 times 1 is negative 1.
01:27
Add.
01:28
Negative 1 times negative 1 is positive 1.
01:32
1.
01:32
Negative 1 times 1 is negative 1.
01:34
We put it here.
01:35
So you're going to multiply these together and put it here.
01:39
0 plus negative 1 is negative 1.
01:42
Negative 1 times negative 1 is a positive 1.
01:45
You're going to put it here.
01:47
Negative 16 plus 1 is a negative 15.
01:51
So that also gives you negative 15.
01:57
When we do 2 minus square to 3, however, you're not going to get negative 15.
02:03
So this one's going to be a little bit longer.
02:06
So i'm going to make this a little longer.
02:08
So 2 minus square root of 3.
02:10
We've got 1, 0, 0, 0, negative 16.
02:15
We're going to bring down the 1.
02:18
2 minus 1, or sorry, 2 times 1 is 2 minus square of 3.
02:23
Then if i add them, i get 2 minus square to 3.
02:27
And i'll do my math down here.
02:29
So i'm going to multiply these together.
02:31
2 minus square to 3 times 2 minus square to 3.
02:36
We're going to foil.
02:38
So that's going to give us two times two is four.
02:42
First, outside is that's minus two square root of three.
02:47
Then i'm going to multiply the insides, which is a minus two square to three.
02:51
And then my last terms, which is plus three...