# Problem of the Week

## Updated at Jan 20, 2014 11:05 AM

This week's problem comes from the algebra category.

How can we compute the factors of $$3{x}^{2}-3x-168$$?

Let's begin!

$3{x}^{2}-3x-168$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$3{x}^{2}$$, $$-3x$$, and $$-168$$?It is $$3$$.2 What is the highest degree of $$x$$ that divides evenly into $$3{x}^{2}$$, $$-3x$$, and $$-168$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$3$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$3$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$3(\frac{3{x}^{2}}{3}+\frac{-3x}{3}-\frac{168}{3})$3 Simplify each term in parentheses.$3({x}^{2}-x-56)$4 Factor $${x}^{2}-x-56$$.1 Ask: Which two numbers add up to $$-1$$ and multiply to $$-56$$?$$-8$$ and $$7$$2 Rewrite the expression using the above.$(x-8)(x+7)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$3(x-8)(x+7)$Done 3*(x-8)*(x+7)