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 12n2+38n−1412{n}^{2}+38n-14?

Let's start!



12n2+38n−1412{n}^{2}+38n-14

1
Find the Greatest Common Factor (GCF).
GCF = 22

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
2(12n22+38n2−142)2(\frac{12{n}^{2}}{2}+\frac{38n}{2}-\frac{14}{2})

3
Simplify each term in parentheses.
2(6n2+19n−7)2(6{n}^{2}+19n-7)

4
Split the second term in 6n2+19n−76{n}^{2}+19n-7 into two terms.
2(6n2+21n−2n−7)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))2(3n(2n+7)-(2n+7))

6
Factor out the common term 2n+72n+7.
2(2n+7)(3n−1)2(2n+7)(3n-1)

Done
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