Transcript Algebra 2
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) 9 z 18 9( z 2)
2) 56m 35p 7(8m 5 p)
3) 12 24 z 12(1 2 z )
Factoring out a number and a variable
1) 9 x 2 12x 3 3x 2 (3 4 x)
3
6
x
3x 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 4m2 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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