Problem of the Week

Updated at Jul 4, 2022 8:55 AM

This week's problem comes from the algebra category.

How would you find the factors of \(15{n}^{2}+10n-5\)?

Let's begin!



\[15{n}^{2}+10n-5\]

1
Find the Greatest Common Factor (GCF).
GCF = \(5\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[5(\frac{15{n}^{2}}{5}+\frac{10n}{5}-\frac{5}{5})\]

3
Simplify each term in parentheses.
\[5(3{n}^{2}+2n-1)\]

4
Split the second term in \(3{n}^{2}+2n-1\) into two terms.
\[5(3{n}^{2}+3n-n-1)\]

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

6
Factor out the common term \(n+1\).
\[5(n+1)(3n-1)\]

Done
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