Factoring Guide
1. Check to see how many ‘terms’ are in the polynomial.
2. Identify what types of factoring can be applied to the number to terms you
have counted.
Always check for a common factor first!!
NUMBER OF
TERMS
TYPE OF FACTORING
EXAMPLES
a) Common Factoring
4r 2t − 24r 3t 2u
=
b) Difference of Squares
Pattern: a 2 − b 2 = (a − b )(a + b )
49a 2 − 16r 2
=
a) Common Factoring
8a 2 − 24a + 40ab
=
b) Trinomial
Pattern: x 2 + bx + c
x 2 + 4x − 32
c) Trinomial
Pattern: ax 2 + bx + c
6x 2 + 5x − 6
Two
Three
d) Perfect Square Trinomial
a 2 + 2ab + b 2
1) Pattern:
= (a + b )2
a 2 − 2ab + b 2
2) Pattern:
= (a − b )2
Four
a) Common factoring
b) Grouping for a common factor
- group (two terms) and (two terms)
c) Grouping for a Difference of
Squares
- group (three terms) and (one)
-three terms are a trinomial square
1) 9x 2 + 12xy + 4y 2
2) 16x 2 − 40xy + 25y 2
ax − by + bx − ay
=
=
=
a 2 − 2ab + b 2 − 25
=
=
=