Steps for Factoring Polynomials
(Remember that a set of terms can be treated as one giant term)
1) Is there a Greatest Common Factor (GCF)? If there is one, pull it out.
2) Now try and factor what is left using the following:
a) Is there a binomal anywhere? If not, go to 2b). If so, can it be factored
by using any of the following rules:
Binomal =
Factored
A2 – B2
=
(A + B)(A – B)
{Difference of Two Squares}
A3 + B3
=
(A + B)(A2 – AB + B2)
{Sum of Two Cubes}
A3 – B3
=
(A – B)(A2 + AB + B2)
{Difference of Two Cubes}
b) Is there a trinomal anywhere? If not, go to 2c). If so,
i. Can it be factored by using any of the following rules:
Trinomal
=
Factored
A2 + 2AB + B2
=
(A + B)2
A2 – 2AB + B2
=
(A – B)2
ii. Can it be factored by trial and error (reverse of FOIL)?
c) Are there more than three terms? If so, can it be broken down into
monomials, binomials and trinomials by grouping? If not, go to 3). If so,
can you group them in such a way that the groups can be easily factored?
3) Repeat 1) and 2) until the polynomial has been factored completely.