Math

For what values of b is the expression factorable?
x^2 + bx + 12

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  1. (x-p)(x-q) = x^2 + b x + 12
    p q = 12
    b = +/-(p+q)
    p and q must be the same sign and product 12
    so
    1) p = 1, q = 12
    2) p = 3, q = 4
    3) p = -1 , q = -12
    4) p = -3, q = -4
    so
    b = 13
    b = -13
    b = 7
    b = -7
    try those
    x^2 + 13 x + 12 = (x+12)(x+1)
    x^2 - 13 x + 12 = (x-12)(x-1)
    x^2 + 7 x + 12 = (x+3)(x+4)
    x^2 - 7 x + 12 = (x-3)(x-4)
    b = -13

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    posted by Damon
  2. Did we forget 2,6 and -2,-6?

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    posted by Steve
  3. Thank you Damon and Steve. Thank you both.

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