Problem of the Week

Updated at Dec 17, 2018 11:09 AM

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Mar 31, 2025

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

How can we factor $36{v}^{2}-48v+15$ ?

Check out the solution below!

36{v}^{2}-48v+15

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

36{v}^{2}

-48v

, and

15

It is

3

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

36{v}^{2}

-48v

, and

15

It is 1, since

v

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{36{v}^{2}}{3}+\frac{-48v}{3}+\frac{15}{3})

Simplify each term in parentheses.

3(12{v}^{2}-16v+5)

Split the second term in

12{v}^{2}-16v+5

into two terms.

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

12\times 5=60

Ask: Which two numbers add up to

-16

and multiply to

60

-6

and

-10

Split

-16v

as the sum of

-6v

and

-10v

12{v}^{2}-6v-10v+5

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

3(12{v}^{2}-6v-10v+5)

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

3(6v(2v-1)-5(2v-1))

Factor out the common term

2v-1

3(2v-1)(6v-5)

Done