A rectangular sheet of cardboard measuring by has squares of side cut from each corner

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

A rectangular sheet of cardboard measuring

24\,\text{cm}

18\,\text{cm}

has squares of side

x\,\text{cm}

cut from each corner. The sides are then folded up to form an open box. Which one of the following polynomials represents the volume

V(x)

(in cubic centimetres) of the box? (a)

4x^{3}+84x^{2}-432x

(b)

4x^{3}-84x^{2}+432x

(c)

x^{3}-42x^{2}+432x

(d)

4x^{3}-96x^{2}+432x