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).
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.
\[6(2{x}^{2}+4x-x-2)\]

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
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