$4{x}^{2}+24x+20$

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Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

4{x}^{2}

24x

, and

20

It is

4

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

4{x}^{2}

24x

, and

20

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

4

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GCF =

4

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

4(\frac{4{x}^{2}}{4}+\frac{24x}{4}+\frac{20}{4})

Simplify each term in parentheses.

4({x}^{2}+6x+5)

Factor

{x}^{2}+6x+5

Ask: Which two numbers add up to

6

and multiply to

5

1

and

5

Rewrite the expression using the above.

(x+1)(x+5)

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4(x+1)(x+5)

Done

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4x2+24x+204{x}^{2}+24x+204x2+24x+20