# Problem of the Week

## Updated at Oct 4, 2021 5:16 PM

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

How would you find the factors of $$4{w}^{2}-4w-8$$?

Here are the steps:

$4{w}^{2}-4w-8$

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