College Algebra Class - Need Help Factoring

I am lost in my college algebra class right now. This semester just started and I have no clue how to factor. Can somebody please help me to understand this.

Example: 2x^2+x-3
Answer: (2x+3)(x-1)

I am absolutely lost on how they got this answer...However, I do know how to FOIL it to get back to the original problem. I just want to know how to do this step-by-step...Please help.

Factoring is easy after you practice a while at it. Like anything else, it just takes practice.

\(\displaystyle 2x^{2}+x-3\)

Now, ask yourself what 2 numbers when multiplied equal -6 and when added equal 1.

That is because we multiply the number in front of the x^2(coefficient) by the constant to get (-3)(2)=-6

Of course, the 1 is the term in front of the x.

Hmmmm...what could they be?. How about 3 and -2?. 3+(-2)=1 and (3)(-2)=-6.

Now, let's put those in place of the x term. Afterall, 3x-2x=x.

\(\displaystyle 2x^{2}+3x-2x-3\)

Group:

\(\displaystyle (2x^{2}+3x)-(2x+3)\)

Factor out something common from each:

\(\displaystyle x(2x+3)-1(2x+3)\)

See there?. What is in the parentheses is the same. That is crucial. It won't work if they're not.

\(\displaystyle \fbox{(2x+3)(x-1)}\)

There we have it. Was that simple enough of an explanation?. Hope it cleared things up a little.

If you're up to it, post another with your workings and let me check it. Mind, I have to leave in a few hours though, but someone else can help if I am not here.

Ever used a google search?

http://www.purplemath.com/modules/solvquad.htm