College Algebra & Trigonometry, 2018a

14 CHAPTER 1. ALGEBRA REVIEW
1.2 Factoring
This section will review three of the most common types of factoring - factoring
out a Greatest Common Factor, Trinomial Factoring and factoring a Difference of
Squares.
Greatest Common Factor
Factoring out a greatest common factor essentially undoes the distributive multiplication
that often occurs in mathematical expressions. This factor may be monomial
or polynomial, but in these examples, we will explore monomial common
factors.
In multiplying 3xy 2 (5x−2y) =15x 2 y 2 −6xy 3 the monomial term 3xy 2 is multiplied
or distributed to both terms inside the parentheses. The process of factorization
undoes this multiplication.
Example:
Factor 7x 2 +14x
This expression has two terms. The coefficients share a common factor of 7 and
the only variable involved in this expression is x. The highest power of the variable
that is shared by both terms is x 1 , so this is the power of x that can be factored
out of both terms. The greatest common factor is 7x.
7x 2 +14x =7x(x +2)
It isn’t necessary to find the greatest common factor right away. In more complicated
problems, the factoring can be accomplished in pieces, similar in fashion to
reducing fractions.