How do you factor #8n^2-9np-14p^2 #?

1 Answer
Aug 28, 2016

Answer:

Use an AC method to find:

#8n^2-9np-14p^2=(8n+7p)(n-2p)#

Explanation:

Given:

#8n^2-9np-14p^2#

Use an AC method:

Look for a pair of factors of #AC=8*14=112# which differ by #B=9#.

Note that in order for the difference of the factors to be odd, one of the factors must be even and the other odd. So we can eliminate most possibilities quickly and find...

The pair #16, 7# works.

Use this pair to split the middle term, then factor by grouping as follows:

#8n^2-9np-14p^2#

#=8n^2-16np+7np-14p^2#

#=(8n^2-16np)+(7np-14p^2)#

#=8n(n-2p)+7p(n-2p)#

#=(8n+7p)(n-2p)#