# Problem of the Week

## Updated at Mar 26, 2018 4:21 PM

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

How can we factor $$8{x}^{2}+2x-28$$?

Here are the steps:

$8{x}^{2}+2x-28$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$8{x}^{2}$$, $$2x$$, and $$-28$$?It is $$2$$.2 What is the highest degree of $$x$$ that divides evenly into $$8{x}^{2}$$, $$2x$$, and $$-28$$?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{2x}{2}-\frac{28}{2})$3 Simplify each term in parentheses.$2(4{x}^{2}+x-14)$4 Split the second term in $$4{x}^{2}+x-14$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$4\times -14=-56$2 Ask: Which two numbers add up to $$1$$ and multiply to $$-56$$?$$8$$ and $$-7$$3 Split $$x$$ as the sum of $$8x$$ and $$-7x$$.$4{x}^{2}+8x-7x-14$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$2(4{x}^{2}+8x-7x-14)$5 Factor out common terms in the first two terms, then in the last two terms.$2(4x(x+2)-7(x+2))$6 Factor out the common term $$x+2$$.$2(x+2)(4x-7)$Done 2*(x+2)*(4*x-7)