Problem of the Week

Updated at Mar 29, 2021 9:12 AM

How can we factor \(36{n}^{2}+6n-12\)?

Below is the solution.



\[36{n}^{2}+6n-12\]

1
Find the Greatest Common Factor (GCF).
GCF = \(6\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[6(\frac{36{n}^{2}}{6}+\frac{6n}{6}-\frac{12}{6})\]

3
Simplify each term in parentheses.
\[6(6{n}^{2}+n-2)\]

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

5
Factor out common terms in the first two terms, then in the last two terms.
\[6(2n(3n+2)-(3n+2))\]

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

Done
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