# 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).1 What is the largest number that divides evenly into $$12{m}^{2}$$, $$-50m$$, and $$42$$?It is $$2$$.2 What is the highest degree of $$m$$ that divides evenly into $$12{m}^{2}$$, $$-50m$$, and $$42$$?It is 1, since $$m$$ is not in every term.3 Multiplying the results above,The GCF is $$2$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!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.1 Multiply the coefficient of the first term by the constant term.$6\times 21=126$2 Ask: Which two numbers add up to $$-25$$ and multiply to $$126$$?$$-7$$ and $$-18$$3 Split $$-25m$$ as the sum of $$-7m$$ and $$-18m$$.$6{m}^{2}-7m-18m+21$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$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 2*(6*m-7)*(m-3)