Problem of the Week

Updated at Apr 8, 2024 1:34 PM

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Mar 31, 2025

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

How would you find the factors of $12{m}^{2}-18m+6$ ?

Check out the solution below!

12{m}^{2}-18m+6

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

12{m}^{2}

-18m

, and

6

It is

6

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

12{m}^{2}

-18m

, and

6

It is 1, since

m

is not in every term.

Multiplying the results above,

The GCF is

6

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

GCF =

6

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

6(\frac{12{m}^{2}}{6}+\frac{-18m}{6}+\frac{6}{6})

Simplify each term in parentheses.

6(2{m}^{2}-3m+1)

Split the second term in

2{m}^{2}-3m+1

into two terms.

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

2\times 1=2

Ask: Which two numbers add up to

-3

and multiply to

2

-1

and

-2

Split

-3m

as the sum of

-m

and

-2m

2{m}^{2}-m-2m+1

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

6(2{m}^{2}-m-2m+1)

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

6(m(2m-1)-(2m-1))

Factor out the common term

2m-1

6(2m-1)(m-1)

Done