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Algebra 2
7.1: Greatest Common Factors; Factoring
by Grouping
Greatest Common Factor
Finding the greatest common factor of a set of
numbers or terms:
1. Find the GCF of the coefficients.
- List the factors if you need too!!!
2. Use the least exponent that appears on each
of the variables or quantities.
Examples: Find the Greatest Common Factor
(a) 12, 18, 30
(b) 9 x 2 y 3 ,15x 4 y
GCF = 6
GCF = 3x2y
Factoring out a number
1) 9z 18  9( z  2)
2) 56m  35 p  7(8m  5 p)
3) 12  24 z  12(1  2 z )
Factoring out a number and a variable
1) 9 x 2  12 x 3  3x 2 (3  4 x)
3
6
x
 3 x  3x(2 x 2  1)
2)
3)  a 3  3a 2  5a  a(a 2  3a  5)
Factor by Grouping
1. Put ( ) around the 1st and 2nd terms, then ( )
around the 3rd and 4th terms. Leave a sign (±)
between the ( ). You may need to rearrange
the terms!!!
2. Find the GCF of each group and factor it out.
- The stuff inside the ( )’s needs to match!!!
- Be careful with the signs!!!
3. Group together the stuff outside the ( )’s, then
put the match right next too it.
Factoring by grouping
1) 2k  2h  jk  jh
(2k  2h)  ( jk  jh)
2(k  h)  j (k  h)
(k  h)( 2  j )
3) 2a 3  a 2  14a  7
2) 3ma  3mb  2ab  2b 2
(3ma  3mb)  (2ab  2b 2 )
3m(a  b)  2b(a  b)
(a  b)(3m  2b)
(2a 3  a 2 )  (14a  7)
4)  16m3  4m 2 p 2  4mp  p 3
(16m 3  4m 2 p 2 )  (4mp  p 3 )
a (2a  1)  7(2a  1)
 4m 2 ( 4m  p 2 )  p ( 4m  p 2 )
(2a  1)( a 2  7)
(4m  p 2 )( 4m 2  p)
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