# Problem of the Week

## Updated at Jul 11, 2022 2:15 PM

This week's problem comes from the algebra category.

How can we factor $$4{z}^{2}-8z-12$$?

Let's begin!

$4{z}^{2}-8z-12$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$4{z}^{2}$$, $$-8z$$, and $$-12$$?It is $$4$$.2 What is the highest degree of $$z$$ that divides evenly into $$4{z}^{2}$$, $$-8z$$, and $$-12$$?It is 1, since $$z$$ is not in every term.3 Multiplying the results above,The GCF is $$4$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$4$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$4(\frac{4{z}^{2}}{4}+\frac{-8z}{4}-\frac{12}{4})$3 Simplify each term in parentheses.$4({z}^{2}-2z-3)$4 Factor $${z}^{2}-2z-3$$.1 Ask: Which two numbers add up to $$-2$$ and multiply to $$-3$$?$$-3$$ and $$1$$2 Rewrite the expression using the above.$(z-3)(z+1)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$4(z-3)(z+1)$Done4*(z-3)*(z+1)