1. A Brief Review of Factoring
Section 6.6
A Brief Review of Factoring

2. Identifying Name and/or Formula
Factoring Organizer
Number of Terms in the Polynomial
Identifying Name and/or Formula
Example
A. Any number of terms
Common factor
The terms have a common factor consisting of a number, a variable, or both
2x2 – 16x = 2x(x – 8)
3x2 + 9y – 12 = 3(x2 + 3y – 4)
4x2y + 2xy2 + xy = xy(4x + 2y + 1)
B. Two terms
Difference of two squares
First and last terms are perfect squares:
a2 – b2 = (a + b)(a – b)
x2 – y2 = (x + y)(x – y)
16x2 – 1 = (4x + 1)(4x – 1)
25y2 – 9x2 = (5y + 3x)(5y – 3x)
C. Three terms
Perfect-square trinomial
a2 + 2ab + b2 = (a + b)2
a2 2ab + b2 = (a  b)2
x2 – 2xy + y2 = (x – y)2
25x2 – 10x + 1 = (5x – 1)2
16x2 + 24x + 9 = (4x + 3)2

3. Identifying Name and/or Formula
Factoring Organizer
Number of Terms in the Polynomial
Identifying Name and/or Formula
Example
D. Three terms
Trinomial of the form x2 + bx + c
It starts with x2. The constants of the two factors are numbers whose product is c and whose sum is b.
x2 – 7x + 12 = (x – 3)(x – 4)
x2 + 11x – 26 = (x + 13)(x – 2)
x2 – 8x – 20 = (x – 10)(x + 2)
E. Three terms
Trinomial of the form ax2 + bx + c
It starts with ax2, where a is any number but 1.
Use trial-and-error or the grouping number method to factor.
F. Four terms
Factor by grouping
Rearrange the order if the first two terms do not have a common factor.
wx – 6yz + 2wy – 3xz
= wx + 2wy – 3xz – 6yz
= w(x + 2y) – 3z(x + 2y)
= (x + 2y)(w – 3z)

4. Example
Factor. a. b.

5. Example
Factor.

6. Example Factor. a. x2 + 4 b. x2 – 10x – 25
There is no way to factor a sum of two squares. The expression cannot be factored it is prime.
The factor pairs are (1)(–25) or (–1)(25) or (–5)(5). None of these pairs add up to –10. The expression is prime.