# 5.5 Factor and Remainder Theorems Recall how to long divide: 776 ÷6 Warm-Up

```Warm-Up
1.) Simplify. (3x-2y3)3
9xy-2
2.) Solve.
x6 - 16x4 - 4x2 + 64 = 0
Dec 4­6:17 PM
5.5 Factor and Remainder Theorems
Recall how to long divide:
776 ÷6
Dec 4­6:11 PM
1
Examples: Divide using polynomial
long division.
1.) (3x2 - 11x - 26)÷(x-5)
Dec 4­6:22 PM
2.) (7x3 + 11x2 + 7x + 5) ÷(x2 +1)
Dec 4­6:25 PM
2
3.) (4x4 + 5x - 4)÷(x2 - 3x - 2)
Dec 4­6:26 PM
Synthetic Division: Alternative
to long division.
-Can only be used when dividing by
a factor of the form x - k.
Examples Divide using synthetic
division.
1.) (4x2 - 13x - 5) ÷(x-2)
Dec 4­6:27 PM
3
2.) (x2 + 9)÷(x-3)
Dec 4­6:28 PM
3.) (x3 - 4x + 6)÷(x+3)
Dec 4­6:29 PM
4
ICE: Divide using long division
AND synthetic division. (Note:
You should get the same answer
for each process.)
(x4 + 4x3 + 16x - 35)÷(x+5)
Dec 4­6:29 PM
Warm-Up
1.) Simplify:
(x4 + 5x3 - 4x + 9) - (6x4 -10x2 + 5x3 - 4)
2.) Factor. 125y3 - 64
(Hint: Difference of Cubes)
Dec 4­6:32 PM
5
Examples: Given polynomial
f(x) and a factor of f(x), factor
f(x) completely.
1.) f(x) = x3 + 6x2 + 5x - 12; x + 4
Dec 4­6:40 PM
2.) f(x) = 3x3 - 2x2 -61x - 20 ; x - 5
Dec 4­6:41 PM
6
Examples: Given polynomial function
f and a zero of f, find the
other zeros.
1.) f(x) = 4x3 - 25x2 -154x + 40 ; 10
Dec 4­6:49 PM
2.) f(x) = 3x3 + 34x2 + 72x - 64 ; -4
Dec 4­6:50 PM
7
3.) f(x) = 5x3 - x2 -18x + 8 ; -2
Dec 4­6:51 PM
Dec 6­9:38 AM
8
```