Problem of the Week

Updated at Nov 15, 2021 12:21 PM

For this week we've brought you this algebra problem.

How can we factor \(18{n}^{2}-6n-4\)?

Here are the steps:



\[18{n}^{2}-6n-4\]

1
Find the Greatest Common Factor (GCF).
GCF = \(2\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[2(\frac{18{n}^{2}}{2}+\frac{-6n}{2}-\frac{4}{2})\]

3
Simplify each term in parentheses.
\[2(9{n}^{2}-3n-2)\]

4
Split the second term in \(9{n}^{2}-3n-2\) into two terms.
\[2(9{n}^{2}+3n-6n-2)\]

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

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

Done
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