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).
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.
\[2(4{x}^{2}+8x-7x-14)\]

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
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