Problem of the Week

Updated at Oct 10, 2022 3:56 PM

Recent Posts

Mar 24, 2025

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

How can we compute the factors of $15{q}^{2}+6q-21$ ?

Here are the steps:

15{q}^{2}+6q-21

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

15{q}^{2}

6q

, and

-21

It is

3

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

15{q}^{2}

6q

, and

-21

It is 1, since

q

is not in every term.

Multiplying the results above,

The GCF is

3

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

GCF =

3

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

3(\frac{15{q}^{2}}{3}+\frac{6q}{3}-\frac{21}{3})

Simplify each term in parentheses.

3(5{q}^{2}+2q-7)

Split the second term in

5{q}^{2}+2q-7

into two terms.

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

5\times -7=-35

Ask: Which two numbers add up to

2

and multiply to

-35

7

and

-5

Split

2q

as the sum of

7q

and

-5q

5{q}^{2}+7q-5q-7

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

3(5{q}^{2}+7q-5q-7)

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

3(q(5q+7)-(5q+7))

Factor out the common term

5q+7

3(5q+7)(q-1)

Done