Problem of the Week

Updated at Oct 18, 2021 8:24 AM

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Mar 24, 2025

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

How can we factor $30{m}^{2}-26m+4$ ?

Check out the solution below!

30{m}^{2}-26m+4

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

30{m}^{2}

-26m

, and

4

It is

2

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

30{m}^{2}

-26m

, and

4

It is 1, since

m

is not in every term.

Multiplying the results above,

The GCF is

2

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

GCF =

2

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

2(\frac{30{m}^{2}}{2}+\frac{-26m}{2}+\frac{4}{2})

Simplify each term in parentheses.

2(15{m}^{2}-13m+2)

Split the second term in

15{m}^{2}-13m+2

into two terms.

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

15\times 2=30

Ask: Which two numbers add up to

-13

and multiply to

30

-3

and

-10

Split

-13m

as the sum of

-3m

and

-10m

15{m}^{2}-3m-10m+2

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

2(15{m}^{2}-3m-10m+2)

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

2(3m(5m-1)-2(5m-1))

Factor out the common term

5m-1

2(5m-1)(3m-2)

Done