Step 3 continuedFollow these steps:
Multiply the leading coefficient and the constantFind factors of that number that add up to the middle coefficientRewrite the middle term using these factorsFactor by using Grouping Method
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Last StepExample
Greatest Common Factor Examples
With a GCF: Without a GCF.
5 4 32 2 4x x x
Has a GCF of32x
212 7 1x x
Has no common factors other than 1
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How to Factor Out a Greatest Common Factor
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5 4 32 2 4x x x
Take the GCF and factor (divide each term by that number).
3 22 ( 2)x x x
Examples with Different Numbers of Terms
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2 Terms 3 Terms 4 Terms
225 4x 2 2x x 3 23 4 12x x x
Factoring Example
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2 8 15
( 5)( 3)
x x
x x
2 8 15
( 5)( 3)
x x
x x
Find factors of last term (15) that add up to middle term (8). (these would be 5 and 3)
Factoring Example
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Multiply the leading coefficient and the constant (12 X 1)Find factors of that number that add up to the middle coefficient (4 and 3)Rewrite the middle term using these factors
Factor by using Grouping Method
212 7 1x x
212 4 3 1x x x
Sum and Difference
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225 4x
(5 2)(5 2)x x
Use the SUM and DIFFERENCE of the two squares.
Grouping Method
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3 2
3 2
2
2
2 16 32
( 2 ) ( 16 32)
( 2) ( 16)( 2)
( 2)( 16)
x x x
x x x
x x x
x x
Group Terms
Factor Each Group
Use Distributive Property