MATH Resources for Academic Success
Methods of Factoring Polynomials
1) Factoring out the Greatest Common Factor (GCF) – Find the GCF of the terms, divide it out of
each term, and write the result as a product.
Ex.:
2) Factoring by Grouping – If the polynomial has 4 terms, factor the GCF from each pair of terms
and, if the left-over binomials are identical, factor out that binomial.
Ex:
3) Factoring a General Trinomial – Use trial and error OR the Master Product /Systematic
method:
Ex: Trial & Error:
Choose the correct product with correct signs that yield the desired polynomial:
= (3x+2)(x-5)
Ex: Master Product (AKA: systematic or “ac” method)
1) Form the Master Product = (lead coefficient) (constant term)
=(3)(-10) = -30
2) Which factors of the MP can be added to obtain the middle
coefficient (coefficient of x)? (-15)(2)=-30 and (-15) + 2 = -13,
so -15 and 2 are the correct pair of numbers.
3) Rewrite the middle term as two terms using these numbers as
coefficients and factor by grouping:
4) Factoring Special Polynomials:
1) Difference of two squares: factors into conjugates
(identical binomials with opposite signs: (a + b)(a - b))
2) Perfect Square Trinomial: factors into identical binomials
3) Factoring sum or difference of two cubes
Formulas: a3 + b3 = (a + b)(a2 - ab + b2)
a3 - b3 = (a - b)(a2 + ab + b2)
Developed by D. Harris for NFCC, ed. 2015
MATH Resources for Academic Success
Checklist To Factor a Polynomial Completely:
1) Is there a GCF? If so, factor it out.
2) Can I factor by grouping? If there are 4 terms,
try grouping.
3) Is it special? If you recognize the polynomial as
a Difference of Squares or Perfect Square
Trinomial, factor it accordingly.
4) Can I factor the trinomial using the Master
Product or Trial & Error methods?
5) Can I go further? Can any of the results be
factored further?
Developed by D. Harris for NFCC, ed. 2015