Problem of the Week

Updated at Mar 29, 2021 9:12 AM

Recent Posts

Apr 12, 2021

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

Below is the solution.

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

Find the Greatest Common Factor (GCF).

GCF = \(6\)

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

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

Simplify each term in parentheses.

\[6(6{n}^{2}+n-2)\]

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

\[6(6{n}^{2}+4n-3n-2)\]

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

\[6(2n(3n+2)-(3n+2))\]

Factor out the common term \(3n+2\).

\[6(3n+2)(2n-1)\]

Done