Problem of the Week

Updated at Aug 18, 2025 1:08 PM

This week we have another algebra problem:

How can we compute the factors of \(6{n}^{2}-10n-4\)?

Let's start!



\[6{n}^{2}-10n-4\]

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.)
\[2(\frac{6{n}^{2}}{2}+\frac{-10n}{2}-\frac{4}{2})\]

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

4
Split the second term in \(3{n}^{2}-5n-2\) into two terms.
\[2(3{n}^{2}+n-6n-2)\]

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

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

Done
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