## Introductory Algebra for College Students (7th Edition)

The factorization of the polynomial: $4x(x-3)(x-4)$, is equivalent to the volume.
Factoring the given polynomial, $4x^{3}-28x^{2}+48x$, we first note that the gcf = $4x$. Factoring it ou, $= 4x(x^{2}-7x+12)$ ... now, searching for factors of 12 whose sum is $-7$, ... we find $-3$ and $-4$ $= 4x(x-3)(x-4)$ Given the dimensions of the box (left in the image), we use Volume = length$\times$width$\times$height Length = $8-2x =$ ... gcf =$-2$ ... $= -2(-4+x)=-2(x-4)$ Width = $6-2x =$ ... gcf =$-2$ ... $= -2(-3+x)=-2(x-3)$ Height = $x$ Volume = $-2(x-4)\cdot[-2(x-3)]\cdot x$ $=(-2)(-2)x(x-4)(x-3)$ $=4x(x-4)(x-3)\qquad$... multiplication is commutative, $= 4x(x-3)(x-4)$ which is equivalent to the factorization of the polynomial,