﻿ Factoring out the Greatest Common Factor
FACTORING OUT THE GREATEST COMMON FACTOR
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
• PRACTICE (online exercises and printable worksheets)
• Some examples are given below.
Want more details, more exercises?
• Not quite ready for this web exercise? Practice finding greatest common factors first:

EXAMPLES:
Question: Factor out the greatest common factor: $\,6x - 8xy\,$
Answer: $2x(3 - 4y)$

Here's what's going on:

 $6x - 8xy$ Ignore the plus/minus signs of the terms for the moment, and find the greatest common factor of $\,6x\,$ and $\,8xy\,$, which is $\,2x\,$. $\cssId{s18}{= \overset{\text{gcf}}{\overbrace{(2x)}}(3)} \cssId{s19}{- \overset{\text{gcf}}{\overbrace{(2x)}}(4y)}$ Rename each term as the greatest common factor, times the remaining factors. Eventually, you won't need to write down this intermediate step. $= (2x)(3 - 4y)$ Use the distributive law, backwards!
Question: Factor out the greatest common factor: $\,3x^2y + 5x^2y^2\,$
Answer: $x^2y(3 + 5y)$

Note:   In the web exercise below, you would input this answer as:   x^2y(3 + 5y)
Notice that exponents are input using the ‘ ^ ’ key.
Variables must appear in the same order as in the original expression, going from left to right.
For example, although   yx^2(3 + 5y)   or   x^2y(5y + 3)   are correct answers, they are not recognized as correct.
Master the ideas from this section