\[3{x}^{2}-9x-12\]

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Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

3{x}^{2}

-9x

, and

-12

It is

3

What is the highest degree of $x$ that divides evenly into

3{x}^{2}

-9x

, and

-12

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

3

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GCF =

3

Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

3(\frac{3{x}^{2}}{3}+\frac{-9x}{3}-\frac{12}{3})

Simplify each term in parentheses.

3({x}^{2}-3x-4)

Factor

{x}^{2}-3x-4

Ask: Which two numbers add up to

-3

and multiply to

-4

-4

and

1

Rewrite the expression using the above.

(x-4)(x+1)

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3(x-4)(x+1)

Done

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