Problem of the Week

Updated at Jan 20, 2014 11:05 AM

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Mar 24, 2025

This week's problem comes from the algebra category.

How can we compute the factors of $3{x}^{2}-3x-168$ ?

Let's begin!

3{x}^{2}-3x-168

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

3{x}^{2}

-3x

, and

-168

It is

3

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

3{x}^{2}

-3x

, and

-168

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{-3x}{3}-\frac{168}{3})

Simplify each term in parentheses.

3({x}^{2}-x-56)

Factor

{x}^{2}-x-56

Ask: Which two numbers add up to

-1

and multiply to

-56

-8

and

7

Rewrite the expression using the above.

(x-8)(x+7)

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3(x-8)(x+7)

Done