Problem of the Week

Updated at Aug 6, 2018 10:10 AM

This week's problem comes from the algebra category.

How would you find the factors of \(12{n}^{2}-10n-42\)?

Let's begin!



\[12{n}^{2}-10n-42\]

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.)
\[2(\frac{12{n}^{2}}{2}+\frac{-10n}{2}-\frac{42}{2})\]

3
Simplify each term in parentheses.
\[2(6{n}^{2}-5n-21)\]

4
Split the second term in \(6{n}^{2}-5n-21\) into two terms.
\[2(6{n}^{2}+9n-14n-21)\]

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

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

Done
Cymath foriOSAndroid