Thread: factoring a trinomial

Hi,

i was wondering if any could tell me the quickest method of factoring this trinomial,

91+24q+-27q^2

thanks

Originally Posted by amcta

Hi,

i was wondering if any could tell me the quickest method of factoring this trinomial,

91+24q+-27q^2

thanks

This requires some thinking outside the box:

First pull out -1:



What we want to do now is apply the grouping technique:

However, we have to manipulate it in such a way so we can use it.

Note that -13*7=-91 and -24=39-63.

Now, let us rewrite the trinomial:



From the red group, factor out a 3q and from the blue group, factor out a -7.

Thus we now have:



Note that both terms have the same factor. Factoring out the blue term, we get:



Hope this makes sense!