Problem of the Week

Updated at Jan 3, 2022 4:21 PM

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

How can we factor \(14{x}^{2}-7x-21\)?

Here are the steps:



\[14{x}^{2}-7x-21\]

1
Find the Greatest Common Factor (GCF).
GCF = \(7\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[7(\frac{14{x}^{2}}{7}+\frac{-7x}{7}-\frac{21}{7})\]

3
Simplify each term in parentheses.
\[7(2{x}^{2}-x-3)\]

4
Split the second term in \(2{x}^{2}-x-3\) into two terms.
\[7(2{x}^{2}+2x-3x-3)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[7(2x(x+1)-3(x+1))\]

6
Factor out the common term \(x+1\).
\[7(x+1)(2x-3)\]

Done
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