Problem of the Week

Updated at Sep 16, 2013 3:19 PM

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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 $8{x}^{2}+68x+84$ ?

Check out the solution below!

8{x}^{2}+68x+84

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

8{x}^{2}

68x

, and

84

It is

4

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

8{x}^{2}

68x

, and

84

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

4

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

GCF =

4

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

4(\frac{8{x}^{2}}{4}+\frac{68x}{4}+\frac{84}{4})

Simplify each term in parentheses.

4(2{x}^{2}+17x+21)

Split the second term in

2{x}^{2}+17x+21

into two terms.

Multiply the coefficient of the first term by the constant term.

2\times 21=42

Ask: Which two numbers add up to

17

and multiply to

42

14

and

3

Split

17x

as the sum of

14x

and

3x

2{x}^{2}+14x+3x+21

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

4(2{x}^{2}+14x+3x+21)

Factor out common terms in the first two terms, then in the last two terms.

4(2x(x+7)+3(x+7))

Factor out the common term

x+7

4(x+7)(2x+3)

Done