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:
$\displaystyle -(27q^2-24q-91)$
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:
$\displaystyle -({\color{red}27q^2+39q}{\color{blue}-63q-91})$
From the red group, factor out a 3q and from the blue group, factor out a -7.
Thus we now have:
$\displaystyle -(3q{\color{blue}(9q+13)}-7{\color{blue}(9q+13)})$
Note that both terms have the same factor. Factoring out the blue term, we get:
$\displaystyle \color{red}\boxed{-(3q-7)(9q+13)}$
Hope this makes sense!