# Problem of the Week

## Updated at Aug 7, 2017 12:35 PM

This week's problem comes from the algebra category.

How can we compute the factors of $$10{x}^{2}-24x+8$$?

Let's begin!

$10{x}^{2}-24x+8$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$10{x}^{2}$$, $$-24x$$, and $$8$$?It is $$2$$.2 What is the highest degree of $$x$$ that divides evenly into $$10{x}^{2}$$, $$-24x$$, and $$8$$?It is 1, since $$x$$ 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{10{x}^{2}}{2}+\frac{-24x}{2}+\frac{8}{2})$3 Simplify each term in parentheses.$2(5{x}^{2}-12x+4)$4 Split the second term in $$5{x}^{2}-12x+4$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$5\times 4=20$2 Ask: Which two numbers add up to $$-12$$ and multiply to $$20$$?$$-2$$ and $$-10$$3 Split $$-12x$$ as the sum of $$-2x$$ and $$-10x$$.$5{x}^{2}-2x-10x+4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(5{x}^{2}-2x-10x+4)$5 Factor out common terms in the first two terms, then in the last two terms.$2(x(5x-2)-2(5x-2))$6 Factor out the common term $$5x-2$$.$2(5x-2)(x-2)$Done 2*(5*x-2)*(x-2)