MTH 100
Greatest Common Factor
Factor By Grouping
Overview
• Factoring is the inverse of multiplying.
• Keep the following ideas in mind:
1. For coefficients, find the largest number (that
will divide all of the coefficients);
2. For common variables, choose the smallest
exponents);
3. Find your “leftovers” by dividing each term
by the GCF.
Examples
40 x y z  15 x y z  30 x y z
2
5 7
5
7 5
 32 p  28 p  12
3
4 6
2
x  7 y x  5  7 x  2 y x  5
Factor By Grouping
• Typically used when the polynomial has four
terms.
• Factor the GCF of the first two terms, then
factor out the GCF of the leftover of the last
two terms (the “leftovers” should be the
same)
• Rearrangement of terms is allowed.
Examples
ab  5a  4b  20
3 x  3 xy  7 x  7 y
2
a  3b  ab  3a
2