Problem of the Week

Updated at Jan 4, 2021 3:18 PM

This week we have another algebra problem:

How can we factor \(8{u}^{2}-20u+12\)?

Let's start!



\[8{u}^{2}-20u+12\]

1
Find the Greatest Common Factor (GCF).
GCF = \(4\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[4(\frac{8{u}^{2}}{4}+\frac{-20u}{4}+\frac{12}{4})\]

3
Simplify each term in parentheses.
\[4(2{u}^{2}-5u+3)\]

4
Split the second term in \(2{u}^{2}-5u+3\) into two terms.
\[4(2{u}^{2}-2u-3u+3)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[4(2u(u-1)-3(u-1))\]

6
Factor out the common term \(u-1\).
\[4(u-1)(2u-3)\]

Done
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