a rectangular box has a volume of V(x)=x^3+13x^2+50x+56 cubic inches. The height of the box is x+7 inches. The width of the box is x+4 inches. Find the length of the box in terms of x.

Answer 1

Divide the cubic equation by (x+7)(x+4), using polynomial long division, or by factoring the cubic.

Hint: In this case, (x+4) and (x+7) are factors of the cubic. Find the third factor.

Second hint:
(x^3 +13x^2 +50x + 56)/(x+4)
= x^2 + 9x + 14
(Now, factor that)

Answer 2

x+2 inches