$3{x}^{3}+21{x}^{2}+36x$

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Examples

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

3{x}^{3}

21{x}^{2}

, and

36x

It is

3

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

3{x}^{3}

21{x}^{2}

, and

36x

It is

x

Multiplying the results above,

The GCF is

3x

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GCF =

3x

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

3x(\frac{3{x}^{3}}{3x}+\frac{21{x}^{2}}{3x}+\frac{36x}{3x})

Simplify each term in parentheses.

3x({x}^{2}+7x+12)

Factor

{x}^{2}+7x+12

Ask: Which two numbers add up to

7

and multiply to

12

3

and

4

Rewrite the expression using the above.

(x+3)(x+4)

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3x(x+3)(x+4)

Done

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3x3+21x2+36x3{x}^{3}+21{x}^{2}+36x3x3+21x2+36x