Problem of the Week

Updated at Oct 17, 2022 11:23 AM

This week we have another algebra problem:

How can we compute the factors of \(12{n}^{2}+38n-14\)?

Let's start!



\[12{n}^{2}+38n-14\]

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.)
\[2(\frac{12{n}^{2}}{2}+\frac{38n}{2}-\frac{14}{2})\]

3
Simplify each term in parentheses.
\[2(6{n}^{2}+19n-7)\]

4
Split the second term in \(6{n}^{2}+19n-7\) into two terms.
\[2(6{n}^{2}+21n-2n-7)\]

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

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

Done
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