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"I'm currently taking a Math Analysis class.  We started reviewing basic factoring from Algebra 2 before starting new material.  I can factor a basic trinomial with the coefficient of x^2 being 1, but if the coefficient is 2 or more, I am not sure how to factor it.  I am able to factor these very easily with a graphing calculator, but I'd like to know how to do it by hand.Homework Statement \nFactor:  2x^2 + 5x - 122. The attempt at a solution\nI know, by using a graphing calculator, that the trinomial factors into (2x-3)(x+4).  I know that if the trinomial were, for instance, x^2 - 2x - 8, one could say the product of 8 and the coefficient of x is 8, and the factors of 8 that when added together result in negative 2 are -4 and +2, therefore the factors of x^2 - 2x - 8 are (x-4)(x+2).  \n\nCan trinomials with coefficients greater than one be factored in a similar way?\n\nUsing the method described above, I come up with a product of 24.  Factors of 24 that result in a sum of 5 when added together are +8 and -3, which by the method I am acquainted with would mean the factors are (x+8)(x-3), but that obviously doesn't equal 2x^2 + 5x - 12 when multiplied.  I know I'm missing a step somewhere.\n\nThanks for the help in advance.  I know this is a simple question, but it plagued me all day."
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