Download Factoring GCF - Mahopac Central School District

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Find the GCF of each set of numbers.
1) 34, 51
2) 36, 72
3) 21, 42, 56
Finding the GCF
For variables that ALL terms have in
common, the GCF is always the smallest
exponent that you have of each variable.
1) x3, x5
2) z4, z2
3) 12a5, 18a2
4) 18xy, 36y2
5) 36x2y, 54 xy2z
6) 12a5c7, 24a3b2c, 18a10b4c3
Factoring Using the GCF
Factoring with a GCF is basically the opposite
of using the distributive property.
4a (3a + 4)
2
12a
+ 16a
Factoring Using the GCF
Now we’re going to start with: 12a2 + 16a
and end up with: 4a (3a + 4)
Steps:
1) Find the GCF of ALL of the terms. The
GCF will be on the outside of the ( ).
2) Divide each original term by the GCF to
get each term inside the ( ).
* You always have to have the same number of
terms inside the ( ) as you started with.
1) FACTOR 25a2 + 15a.
Find the GCF and divide each term
25a2 + 15a = 5a ( ___ + ___ )
Check your answer by distributing.
2)
Factor 18x2 – 12x3.
Divide each term by the GCF
18x2 - 12x3 = 6x2 ( ___ – ___ )
Check your answer by distributing.
3)
Factor 28a2b + 56abc2.
28a2b + 56abc2 = 28ab ( __ + ___ )
Check your answer by distributing.
4) Factor 28a2 + 21b – 35b2c2
28a2 + 21b - 35b2c2 = 7 ( ___ + ___ – ____ )
Check your answer by distributing.
Factor
2
3x y
–
5
3
27x y z
+
3
7
2
18x y z
Factor
1.
2.
3.
4.
2
16xy
2y2(8x – 12z + 20)
4y2(4x – 6z + 10)
8y2(2x - 3z + 5)
8xy2z(2 – 3 + 5)
-
2
24y z
+
2
40y
Factor
1.
2.
3.
4.
x(20 – 24y)
2x(10x – 12y)
4(5x2 – 6xy)
4x(5x – 6y)
2
20x
- 24xy
Homework
Chapter 9 Packet
Pgs. 529 #’s 1 – 12