Problem of the Week

Updated at Nov 11, 2024 12:01 PM

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May 5, 2025

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

How would you find the factors of $42{t}^{2}+7t-49$ ?

Here are the steps:

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

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

42{t}^{2}

7t

, and

-49

It is

7

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

42{t}^{2}

7t

, and

-49

It is 1, since

t

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

Simplify each term in parentheses.

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

Split the second term in

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

into two terms.

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

6\times -7=-42

Ask: Which two numbers add up to

1

and multiply to

-42

7

and

-6

Split

t

as the sum of

7t

and

-6t

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

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

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

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

7(t(6t+7)-(6t+7))

Factor out the common term

6t+7

7(6t+7)(t-1)

Done