# Problem of the Week

## Updated at Aug 21, 2017 5:11 PM

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

How can we compute the factors of $$8{x}^{2}-22x+12$$?

Here are the steps:

$8{x}^{2}-22x+12$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$8{x}^{2}$$, $$-22x$$, and $$12$$?It is $$2$$.2 What is the highest degree of $$x$$ that divides evenly into $$8{x}^{2}$$, $$-22x$$, and $$12$$?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{8{x}^{2}}{2}+\frac{-22x}{2}+\frac{12}{2})$3 Simplify each term in parentheses.$2(4{x}^{2}-11x+6)$4 Split the second term in $$4{x}^{2}-11x+6$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$4\times 6=24$2 Ask: Which two numbers add up to $$-11$$ and multiply to $$24$$?$$-3$$ and $$-8$$3 Split $$-11x$$ as the sum of $$-3x$$ and $$-8x$$.$4{x}^{2}-3x-8x+6$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(4{x}^{2}-3x-8x+6)$5 Factor out common terms in the first two terms, then in the last two terms.$2(x(4x-3)-2(4x-3))$6 Factor out the common term $$4x-3$$.$2(4x-3)(x-2)$Done 2*(4*x-3)*(x-2)