Factoring tricky trinomial

Charchar · #1 $Old$ November 13th, 2009, 11:16 PM

I am stumped on a trinomial problem that is of the form x^2+bx+c.
(a+b)^2+9(a+b)-10

I am not sure how to go about this because prior to this question, I was only asked to factor a trinomial into a product of two binomials...the answer key says this should work out to two trinomials.

Bacterius · #2 $Old$ November 13th, 2009, 11:33 PM

Consider $x = a + b$ , makes things a lot easier, because you get :

$x^2 + 9x - 10 = 0$

Now ...

$10 = 10 \times 1$

$9 = 10 - 1$

The factorization would then be :
$(x - 10)(1 - x) = 0$

Now replace $x$ by $(a + b)$ :

$(a + b - 10)[1 - (a + b)] = 0$

$(a + b - 10)(1 - a - b) = 0$

This is how I would have done it since I do not get what you mean by "a product of two binomials" or even less "should work out to two trinomials".

Charchar · #3 $Old$ November 14th, 2009, 12:07 AM

Thank you very much! Yes, I knew (a+b) was x, yet, even knowing that I still didnt know what to do. Thanks again for showing me how!

Bacterius · #4 $Old$ November 14th, 2009, 01:44 AM

Quote:

Originally Posted by Charchar $View Post$

Thank you very much! Yes, I knew (a+b) was x, yet, even knowing that I still didnt know what to do. Thanks again for showing me how!

No problem ! Factorizing expressions can seem a bit difficult and random at first but as you do more, you get better and better.