CP Algebra II 10/29/15
Factoring Patterns
Name: _____________________
Zero Product Property:
For any real numbers a and b, if ab = 0, then either a = 0, b = 0, or both a and b equal zero.
Ex #1: Solve the equation: (x + 3)(x - 5) = 0
Ex #2: Solve the equation: 20x 2 +15x = 0
Sometimes it is useful to rewrite a polynomial as the product of its factors.
This rewriting is called factoring.
This table summarizes some of the most common factoring techniques used with polynomials.
Number of Terms
Factoring Technique
General Case
Any number
Greatest Common Factor
(GCF)
a 3b 2 + 2a 2b - 4ab 2 = ab a2b + 2a - 4b
Two
Difference of Two Squares
a2 - b2 = ( a + b ) ( a - b )
Three
Perfect Square Trinomials
a 2 + 2ab + b2 = ( a + b )
(
a 2 - 2ab + b2 = ( a - b )
2
2
)
acx 2 + ( ad + bc ) x + bd = ( ax + b ) ( cx + d )
General Trinomials
Example 1:
a.
2xy 3 - 10x
Example 2:
a.
a.
6x 2 y2 - 2xy2 + 6x 3 y
b.
16a2 - 25b2
Factor the Perfect Square Trinomials.
x 2 + 12x + 36
Example 4:
b.
Factor the Difference of Two Squares.
9x 2 - 4y 2
Example 3:
a.
Factor the GCF.
b.
9x 2 - 30x + 25
b.
6x 2 + 71x - 12
Factor the General Trinomials.
x 2 - 2x - 15
c.
x 2 + x - 42
d.
12m2 - m - 6
Example 5:
Factor.
a.
3x 2 - 27y2
b.
3z 2 + 24z + 45
c.
x 3 - 8x 2 + 15x
d.
3p 3 - 12 pq 2
e.
3a 3 + 12a2 - 63a
f.
a 4 - 16
Example 6:
a.
Solve. (These are similar to your homework problems)
x 2 -2x -15 = 0
b.
9x 2 +3x = 0