Problem of the Week

Updated at May 28, 2018 10:29 AM

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Mar 24, 2025

To get more practice in algebra, we brought you this problem of the week:

How can we compute the factors of $2{x}^{2}-10x-28$ ?

Check out the solution below!

2{x}^{2}-10x-28

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

2{x}^{2}

-10x

, and

-28

It is

2

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

2{x}^{2}

-10x

, and

-28

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

2

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

GCF =

2

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

2(\frac{2{x}^{2}}{2}+\frac{-10x}{2}-\frac{28}{2})

Simplify each term in parentheses.

2({x}^{2}-5x-14)

Factor

{x}^{2}-5x-14

Ask: Which two numbers add up to

-5

and multiply to

-14

-7

and

2

Rewrite the expression using the above.

(x-7)(x+2)

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

2(x-7)(x+2)

Done