THE
FACTORING
TOOLBOX
Use the “lightweight” tools
before you get out “the hammer.”
1. Greatest Common Factor (GCF):
Factored Form = (GCF)(“Leftovers”)
If the polynomial is a binomial, try:
2. Difference of Squares (DS):
a 2  b2  (a  b)(a  b)
3. Sum of Cubes (SC):
a3  b3  (a  b)(a 2  ab  b2 )
4. Difference of Cubes DC):
a3  b3  (a  b)(a 2  ab  b2 )
If the polynomial is a trinomial, try:
5. Perfect Square Trinomial (PST)
a 2  2ab  b2  (a  b)2
a 2  2ab  b2  (a  b)2
6. General Method (GM)
Given polynomial with quadratic coefficient = 1:
x 2  bx  c
find factor pair whose product = c and whose sum = b.
7. General Method with Grouping (GMG)
Given polynomial with quadratic coefficient  0 or 1:
ax2  bx  c
(See separate handout for detailed method)
If the polynomial has more than 3 terms, try:
8. Factoring by Grouping:
Group given terms into pieces that can be factored using a
combination of the above methods.