Problem of the Week

Updated at Mar 9, 2020 5:14 PM

To get more practice in algebra, we brought you this problem of the week:

How can we compute the factors of \(28{p}^{2}-14p-14\)?

Check out the solution below!



\[28{p}^{2}-14p-14\]

1
Find the Greatest Common Factor (GCF).
GCF = \(14\)

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
\[14(\frac{28{p}^{2}}{14}+\frac{-14p}{14}-\frac{14}{14})\]

3
Simplify each term in parentheses.
\[14(2{p}^{2}-p-1)\]

4
Split the second term in \(2{p}^{2}-p-1\) into two terms.
\[14(2{p}^{2}+p-2p-1)\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[14(p(2p+1)-(2p+1))\]

6
Factor out the common term \(2p+1\).
\[14(2p+1)(p-1)\]

Done
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