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 28p2−14p−1428{p}^{2}-14p-14?

Check out the solution below!



28p2−14p−1428{p}^{2}-14p-14

1
Find the Greatest Common Factor (GCF).
GCF = 1414

2
Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)
14(28p214+−14p14−1414)14(\frac{28{p}^{2}}{14}+\frac{-14p}{14}-\frac{14}{14})

3
Simplify each term in parentheses.
14(2p2−p−1)14(2{p}^{2}-p-1)

4
Split the second term in 2p2−p−12{p}^{2}-p-1 into two terms.
14(2p2+p−2p−1)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))14(p(2p+1)-(2p+1))

6
Factor out the common term 2p+12p+1.
14(2p+1)(p−1)14(2p+1)(p-1)

Done
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