Best Answer:
Try it this way: Look for factors of 2*-3 = -6 that add to 5. These are 6 and -1. So now rewrite your middle term, 5x, as --x + 6x, so you have 2x^2 - x + 6x - 3. Now group each side: (2x^2 - x) + (6x-3) and factor: x(2x-1) + 3(2x-1). Now factor out the common (2x-1) factor: (2x-1)(x+3).

This technique is called "splitting-the-middle," as it splits the middle term of the expression. It helps take some of the trial-and-error out of factoring these types of quadratics. In general, for Ax^2 + Bx + C, you look for factors of A*C that sum to B. Then rewrite the middle term as the sum of those two numbers, group, factor, and factor again. You'll always come up with a product of binomials.

To help reinforce your understanding of these concepts, I've searched and found a webpage and a video tutorial that address problems similar to this one, and I thought they might be helpful to you. I've listed them below.

Source(s):
http://www.teacherschoice.com.au/sample_help_1_alg.htm

http://www.youtube.com/watch?v=Od38CRJNC5w

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