Problem of the Week

Updated at Oct 24, 2022 12:52 PM

How would you find the factors of \(12{n}^{2}-36n-21\)?

Below is the solution.



\[12{n}^{2}-36n-21\]

1
Find the Greatest Common Factor (GCF).
GCF = \(3\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[3(\frac{12{n}^{2}}{3}+\frac{-36n}{3}-\frac{21}{3})\]

3
Simplify each term in parentheses.
\[3(4{n}^{2}-12n-7)\]

4
Split the second term in \(4{n}^{2}-12n-7\) into two terms.
\[3(4{n}^{2}+2n-14n-7)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[3(2n(2n+1)-7(2n+1))\]

6
Factor out the common term \(2n+1\).
\[3(2n+1)(2n-7)\]

Done
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