# Problem of the Week

## Updated at Oct 23, 2017 3:21 PM

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

How can we factor $$12{x}^{2}+18x-12$$?

Here are the steps:

$12{x}^{2}+18x-12$

 1 Find the Greatest Common Factor (GCF).1 What is the largest number that divides evenly into $$12{x}^{2}$$, $$18x$$, and $$-12$$?It is $$6$$.2 What is the highest degree of $$x$$ that divides evenly into $$12{x}^{2}$$, $$18x$$, and $$-12$$?It is 1, since $$x$$ is not in every term.3 Multiplying the results above,The GCF is $$6$$.To get access to all 'How?' and 'Why?' steps, join Cymath Plus!GCF = $$6$$2 Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)$6(\frac{12{x}^{2}}{6}+\frac{18x}{6}-\frac{12}{6})$3 Simplify each term in parentheses.$6(2{x}^{2}+3x-2)$4 Split the second term in $$2{x}^{2}+3x-2$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$2\times -2=-4$2 Ask: Which two numbers add up to $$3$$ and multiply to $$-4$$?$$4$$ and $$-1$$3 Split $$3x$$ as the sum of $$4x$$ and $$-x$$.$2{x}^{2}+4x-x-2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$6(2{x}^{2}+4x-x-2)$5 Factor out common terms in the first two terms, then in the last two terms.$6(2x(x+2)-(x+2))$6 Factor out the common term $$x+2$$.$6(x+2)(2x-1)$Done 6*(x+2)*(2*x-1)