Problem of the Week

Updated at Apr 23, 2018 11:41 AM

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Mar 31, 2025

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

How can we compute the factors of $49{x}^{2}+7x-42$ ?

Here are the steps:

49{x}^{2}+7x-42

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

49{x}^{2}

7x

, and

-42

It is

7

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

49{x}^{2}

7x

, and

-42

It is 1, since

x

is not in every term.

Multiplying the results above,

The GCF is

7

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GCF =

7

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

7(\frac{49{x}^{2}}{7}+\frac{7x}{7}-\frac{42}{7})

Simplify each term in parentheses.

7(7{x}^{2}+x-6)

Split the second term in

7{x}^{2}+x-6

into two terms.

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

7\times -6=-42

Ask: Which two numbers add up to

1

and multiply to

-42

7

and

-6

Split

x

as the sum of

7x

and

-6x

7{x}^{2}+7x-6x-6

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

7(7{x}^{2}+7x-6x-6)

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

7(7x(x+1)-6(x+1))

Factor out the common term

x+1

7(x+1)(7x-6)

Done