# Problem of the Week

## Updated at Jun 3, 2024 5:50 PM

This week's problem comes from the algebra category.

How can we compute the factors of $$8{w}^{2}-24w+18$$?

Let's begin!

$8{w}^{2}-24w+18$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$8{w}^{2}$$, $$-24w$$, and $$18$$?It is $$2$$.2 What is the highest degree of $$w$$ that divides evenly into $$8{w}^{2}$$, $$-24w$$, and $$18$$?It is 1, since $$w$$ 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{8{w}^{2}}{2}+\frac{-24w}{2}+\frac{18}{2})$3 Simplify each term in parentheses.$2(4{w}^{2}-12w+9)$4 Rewrite $$4{w}^{2}-12w+9$$ in the form $${a}^{2}-2ab+{b}^{2}$$, where $$a=2w$$ and $$b=3$$.$2({(2w)}^{2}-2(2w)(3)+{3}^{2})$5 Use Square of Difference: $${(a-b)}^{2}={a}^{2}-2ab+{b}^{2}$$.$2{(2w-3)}^{2}$Done2*(2*w-3)^2