Problem of the Week

Updated at Dec 25, 2017 9:49 AM

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Mar 24, 2025

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

How would you find the factors of $14{x}^{2}-42x+28$ ?

Check out the solution below!

14{x}^{2}-42x+28

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

14{x}^{2}

-42x

, and

28

It is

14

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

14{x}^{2}

-42x

, and

28

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

14

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

GCF =

14

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

14(\frac{14{x}^{2}}{14}+\frac{-42x}{14}+\frac{28}{14})

Simplify each term in parentheses.

14({x}^{2}-3x+2)

Factor

{x}^{2}-3x+2

Ask: Which two numbers add up to

-3

and multiply to

2

-2

and

-1

Rewrite the expression using the above.

(x-2)(x-1)

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

14(x-2)(x-1)

Done