Problem of the Week

Updated at Oct 10, 2022 3:56 PM

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

How can we compute the factors of \(15{q}^{2}+6q-21\)?

Here are the steps:



\[15{q}^{2}+6q-21\]

1
Find the Greatest Common Factor (GCF).
GCF = \(3\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[3(\frac{15{q}^{2}}{3}+\frac{6q}{3}-\frac{21}{3})\]

3
Simplify each term in parentheses.
\[3(5{q}^{2}+2q-7)\]

4
Split the second term in \(5{q}^{2}+2q-7\) into two terms.
\[3(5{q}^{2}+7q-5q-7)\]

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

6
Factor out the common term \(5q+7\).
\[3(5q+7)(q-1)\]

Done
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