Arturo O. answered • 06/22/16

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I would start by multiplying factors containing the 3 given roots, and then multiply by an unknown real number a:

f(x) = a(x+3)(x+1)(x-4)

f(-2) = 24 = a(-2+3)(-2+1)(-2-4) = a(1)(-1)(-6) = 6a

6a = 24, so a = 24/6 = 4

Final answer:

f(x) = 4(x+3)(x+1)(x-4)

Note this has 3 roots: -3,-1,4; and f(-2) = 24, and the coefficients are real.