(08.03 mc) factor completely 2x2 + 2x − 24. (5 points) 2(x − 3)(x + 4) (2x − 3)(x + 8) 2(x − 4)(x + 6) (2x − 6)(x + 4

Answer

2(x + 4)(x - 3)

The trick here is to notice that all 3 terms can be div. by 2:

2(x^2 + x - 12)

Note that -12 factors into -3 * 4 or -4 * 3.  The pair {4, -3} leads to the correct sign for the middle term of the product.  

x^2 + x - 12 = (x + 4)(x - 3), and so 2x2 + 2x − 24 = 2(x + 4)(x - 3).