# Problem of the Week

## Updated at Jun 17, 2019 9:47 AM

How can we compute the factors of $$2{m}^{2}-8m-24$$?

Below is the solution.

$2{m}^{2}-8m-24$

 1 How?Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$2{m}^{2}$$, $$-8m$$, and $$-24$$?It is $$2$$.2 What is the highest degree of $$m$$ that divides evenly into $$2{m}^{2}$$, $$-8m$$, and $$-24$$?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{2{m}^{2}}{2}+\frac{-8m}{2}-\frac{24}{2})$3 Simplify each term in parentheses.$2({m}^{2}-4m-12)$4 How?Factor $${m}^{2}-4m-12$$.1 Ask: Which two numbers add up to $$-4$$ and multiply to $$-12$$?$$-6$$ and $$2$$2 Rewrite the expression using the above.$(m-6)(m+2)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(m-6)(m+2)$Done2*(m-6)*(m+2)