# SOLUTION: how do you factor 2x^2+9x-5 i have a summer math packet and im SO CONFUSED on factoring. please and thank you.

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 Question 485408: how do you factor 2x^2+9x-5 i have a summer math packet and im SO CONFUSED on factoring. please and thank you.Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!``` There are two methods. The trial and error method and the "ac"-method. When a trinomial starts or ends with a prime number or 1, the trial and error method is easier. In your problem both 2 and 5 are prime, so the trial-and-error method is easier. I'll show it here. However, if you want to learn the ac-method, go here: http://www.algebra.com/my/change_this_name32371.lesson?content_action=show_dev Factor 2x²+9x-5 It's the reverse of FOIL The first coefficient is 2. The only way to factor that first coefficient, 2, is as 2·1 The constant (ignoring signs) is 5. The only way to factor 5 is as 5·1 So the incomplete factorization without the signs has to be one of these two: (2x 5)(x 1) or (2x 1)(x 5) ----- For (2x 5)(x 1), if we used FOIL, the OUTERS and INNERS would be 2x and 5x, but there is NO way to assign signs to them so that when they are combined they would give the middle term +9x. So that is not the right form. For (2x 1)(x 5), if we used FOIL the OUTERS and INNERS would be 10x and 1x, and there IS a way to assign signs to them so that when they are combined they would give the middle term +9x. So we have to assign the 10x a + sign and the 1x a - sign. The 10x comes from the OUTERS so we put a + before the 5, and we put a - sign before the 1: Answer: (2x - 1)(x + 5) Check by multiplying it out by FOIL: 2x² + 10x - 1x - 5 2x² + 9x - 5 That's the original trinomial, so we are correct. Edwin```