# Thread: Tips on factoring, a not equal to 1

1. ## Tips on factoring, a not equal to 1

Hi everyone!

I am going in for a job interview in the math lab at school and in the interview I'm going to be asked about 7-10 questions from these areas:

Basic Arithmetic
Intro/Intermediate Algebra
College Algebra
Calculus I

The thing I'm really concerned about that I always end up slipping on factoring trinomials when the leading coefficient is not 1.

I remember my algebra teacher taught me a way that you could multiply together the leading coefficient and the constant term, then find factors of that and do something with those factors....does anyone know what I'm talking about?

Let's take for example the trinomial $6x^2+11x+3$

Does anyone know what method I'm referring to..or if you have an easier way with some more examples...any help is much appreciated!

My interview is on Tuesday by the way, and I'm going to be practicing problems like crazy! If anyone wants to throw some more basic problems at me from the subjects I listed above, feel free to; I need all the practice I can get!

PS: mods, feel free to move this thread if you think it would be better in another area!

2. For the general $ax^{2} + bx + c$, I find two factors such that they multiply to $ac$ and add up to $b$.

For your example: $6x^{2} + 11x + 3$

Find two factors that multiply to (6)(3) = 18 and that add up to 11. 9 and 2 should come up.

Now, split 11x into 9x + 2x (that's where your factors come in):
$6x^{2} + 11x + 3 = \underbrace{6x^{2} {\color{blue}+ 2x} }_{\text{Factor}} {\color{blue} +} \underbrace{{\color{blue} 9x} + 3}_{\text{Factor}}$
$= 2x{\color{red}(3x+ 1)} + 3{\color{red}(3x+ 1)}$
$= {\color{red}(3x+ 1)}(2x + 3)$