\[12{x}^{3}+11{x}^{2}+2x\]

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Examples

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

12{x}^{3}

11{x}^{2}

, and

2x

It is

1

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

12{x}^{3}

11{x}^{2}

, and

2x

It is

x

Multiplying the results above,

The GCF is

x

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GCF =

x

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

x(\frac{12{x}^{3}}{x}+\frac{11{x}^{2}}{x}+\frac{2x}{x})

Simplify each term in parentheses.

x(12{x}^{2}+11x+2)

Split the second term in

12{x}^{2}+11x+2

into two terms.

Multiply the coefficient of the first term by the constant term.

12\times 2=24

Ask: Which two numbers add up to

11

and multiply to

24

8

and

3

Split

11x

as the sum of

8x

and

3x

12{x}^{2}+8x+3x+2

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x(12{x}^{2}+8x+3x+2)

Factor out common terms in the first two terms, then in the last two terms.

x(4x(3x+2)+(3x+2))

Factor out the common term

3x+2

x(3x+2)(4x+1)

Done

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