00:01
Here we have function h of x, and we're going to use it to find several different function values using synthetic division, and then we'll verify using a different method.
00:10
So for h of 3, we put 3 outside the box, and then we have the coefficients of h of x in a row, 1x cubed, negative 5x squared, negative 7x, and 4.
00:21
We bring down the first number.
00:23
We multiply it by 3, write it in the next space, and add the column.
00:27
We multiply this by 3, negative 6, write it in the next space and add the column.
00:31
Negative 13.
00:33
We multiply this by 3, negative 39, write it in the next space and add the column, negative 35.
00:39
So negative 35 is the remainder, so it's also the function value.
00:43
So h of 3 is negative 35.
00:49
Same idea for part b, we're going to find h of 2, so 2 goes outside the box, and we have 1, negative 5, negative 7, and 4.
00:57
Bring down the 1, multiply it by 2, we get 2, write it in the next space and add.
01:02
Multiply negative 3 by 2, we get negative 6, write it in the next space and add.
01:07
Multiply negative 13 by 2, we get negative 26, right it in the next space and add, we get negative 22.
01:14
So negative 22 is a remainder, so it's the function value.
01:18
So h of 2 is negative 22.
01:23
We're going to keep going for parts c and d.
01:26
So in part c we're finding h of negative 2.
01:33
So negative 2 goes outside the box, and then we have 1, negative 5, negative 7, and 4.
01:43
Bring down the 1, multiply it by negative 2.
01:45
Write it in the next space and add the column, we have negative 7.
01:49
Multiply that by negative 2, we get 14.
01:51
Write it in the next space and add the column, we get 7.
01:54
Multiply that by negative 2, we get negative 14...