Problem of the Week

Updated at Aug 4, 2025 5:00 PM

This week's problem comes from the algebra category.

How can we factor \(12{m}^{2}-34m+20\)?

Let's begin!



\[12{m}^{2}-34m+20\]

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.)
\[2(\frac{12{m}^{2}}{2}+\frac{-34m}{2}+\frac{20}{2})\]

3
Simplify each term in parentheses.
\[2(6{m}^{2}-17m+10)\]

4
Split the second term in \(6{m}^{2}-17m+10\) into two terms.
\[2(6{m}^{2}-5m-12m+10)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(m(6m-5)-2(6m-5))\]

6
Factor out the common term \(6m-5\).
\[2(6m-5)(m-2)\]

Done
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