Philip P. answered • 10/18/17

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V(x) = x

^{3}+ 2x^{2}- 11x - 12To factor, you want 3 numbers that multiply to give -12 (the constant term) and add to give 2 (coefficient of the x

^{2}term). The answer is 4, -3, and 1: (4)(-3)(1) = -12, 4 + (-3) + 1 = 2. So the volume polynomial factors to:V(x) = (x+4)(x-3)(x+1)

Now the volume of a rectangular box is:

V = Length*Width*Height = (x+4)(x-3)(x+1)

So let's pick height = (x+1) = 4.5 (you could pick any one of the three factors).

x+1 = 4.5

x = 3.5

Length = (x+4) = 3.5+4 = 7.5

Width = (x-3) = 3.5 - 3 = 0.5

The box's dimensions are 7.5 m by 0.5 m by 4.5 m