college algebra

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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.

  • algebra -

    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)

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