1. ## factoring a trinomial

Hi,

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

91+24q+-27q^2

thanks

2. 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:

$-(27q^2-24q-91)$

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:

$-({\color{red}27q^2+39q}{\color{blue}-63q-91})$

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

Thus we now have:

$-(3q{\color{blue}(9q+13)}-7{\color{blue}(9q+13)})$

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

$\color{red}\boxed{-(3q-7)(9q+13)}$

Hope this makes sense!