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• The process of finding polynomials whose
product equals a given polynomial is
called factoring.

• Prime polynomial: A polynomial with
variable terms that cannot be written as a
product of two polynomials of lower

Factoring Out the Greatest Common Factor

Factoring by Grouping

When a polynomial has more than three terms, it
can sometimes be factored by grouping.

Factoring Trinomials

Factoring trinomials requires using the FOIL
method in reverse.
To factor ax2 + bx + c we find integers a1, a2, c1,
and c2 such that:

where a1 and a2 are factors of a, and c1 and c2 are
factors of c.

Perfect Square Trinomials

Factoring Special Binomials

Difference of Squares: x2 - y2 = (x + y)(x - y)
Sum of Cubes: x3 + y3 = (x + y)(x2 - xy + y3)
Difference of Cubes: x3 + y3 = (x - y)(x2 + xy + y3)

Check by multiplying.

Check by multiplying.