Problem of the Week

Updated at Oct 4, 2021 5:16 PM

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Mar 24, 2025

For this week we've brought you this algebra problem.

How would you find the factors of $4{w}^{2}-4w-8$ ?

Here are the steps:

4{w}^{2}-4w-8

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

4{w}^{2}

-4w

, and

-8

It is

4

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

4{w}^{2}

-4w

, and

-8

It is 1, since

w

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{w}^{2}}{4}+\frac{-4w}{4}-\frac{8}{4})

Simplify each term in parentheses.

4({w}^{2}-w-2)

Factor

{w}^{2}-w-2

Ask: Which two numbers add up to

-1

and multiply to

-2

-2

and

1

Rewrite the expression using the above.

(w-2)(w+1)

To get access to all 'How?' and 'Why?' steps, join Cymath Plus!

4(w-2)(w+1)

Done