Problem of the Week

Updated at Sep 20, 2021 1:11 PM

For this week we've brought you this algebra problem.

How can we compute the factors of \(12{m}^{2}-50m+42\)?

Here are the steps:



\[12{m}^{2}-50m+42\]

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.)
\[2(\frac{12{m}^{2}}{2}+\frac{-50m}{2}+\frac{42}{2})\]

3
Simplify each term in parentheses.
\[2(6{m}^{2}-25m+21)\]

4
Split the second term in \(6{m}^{2}-25m+21\) into two terms.
\[2(6{m}^{2}-7m-18m+21)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[2(m(6m-7)-3(6m-7))\]

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

Done
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