Problem of the Week

Updated at Apr 23, 2018 11:41 AM

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

How can we compute the factors of \(49{x}^{2}+7x-42\)?

Here are the steps:



\[49{x}^{2}+7x-42\]

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.)
\[7(\frac{49{x}^{2}}{7}+\frac{7x}{7}-\frac{42}{7})\]

3
Simplify each term in parentheses.
\[7(7{x}^{2}+x-6)\]

4
Split the second term in \(7{x}^{2}+x-6\) into two terms.
\[7(7{x}^{2}+7x-6x-6)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[7(7x(x+1)-6(x+1))\]

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

Done
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