Greatest+Common+Factor+(GCF)

Factoring Out the GCF

The Greatest Common Factor of the terms in a quadratic expression is the largest constant, variable, or product of a constant and variable that can go into each term.

Factoring out the GCF can only be used when there is a greatest common factor within all of the elements of the equations.

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How to determine the GCF: Check each element to see if they have a common factor that they're divisible by, then determine the largest factor possible.

Examples...3x 2 -6x+24

1st step-find the number, variable, or constant that each item in the quadratic equation is divisible by.(3)

2nd step-divide each term by the GCF you found.(3x 2 /3=x 2, -6x/3=2x, 24/3=8) (x 2 -2x+8)

3rd step-place the GCF on the outside of the parenthesis of the product=3(x 2 -2x+8)

9x 2 +18x

The GCF is 9x.

9x 2 /9x=x, 18x/9x=2 (x+2)

9x(x+2)

For any problem, check your answer by multiplication.