Problem of the Week

Updated at Jan 4, 2021 3:18 PM

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Mar 24, 2025

This week we have another algebra problem:

How can we factor $8{u}^{2}-20u+12$ ?

Let's start!

8{u}^{2}-20u+12

Find the Greatest Common Factor (GCF).

What is the largest number that divides evenly into

8{u}^{2}

-20u

, and

12

It is

4

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

8{u}^{2}

-20u

, and

12

It is 1, since

u

is not in every term.

Multiplying the results above,

The GCF is

4

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GCF =

4

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

4(\frac{8{u}^{2}}{4}+\frac{-20u}{4}+\frac{12}{4})

Simplify each term in parentheses.

4(2{u}^{2}-5u+3)

Split the second term in

2{u}^{2}-5u+3

into two terms.

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

2\times 3=6

Ask: Which two numbers add up to

-5

and multiply to

6

-2

and

-3

Split

-5u

as the sum of

-2u

and

-3u

2{u}^{2}-2u-3u+3

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4(2{u}^{2}-2u-3u+3)

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

4(2u(u-1)-3(u-1))

Factor out the common term

u-1

4(u-1)(2u-3)

Done