Question

Can someone help me please? Thanks :)

The volume in cubic feet of a box can be expressed as `(x)=x^3-6x^2+8x` , or as the product of three linear factors with integer coefficients. The width of the box is `x-2`.

Factor the polynomial to find linear expressions for the height and the length. Show your work.

Answer 1

see below

Explanation:

`Vol=x^3-6x+8x`

To express a three linear factors we start the process by looking for common factors in all three terms.

We note that `x` is a common factor

`Vol=x(x^2-6+8x)`

The bracket is a quadratic which will factorise into two brackets

`Vol=x(x-2)(x-4)`

width is given as `(x-2)`

The length is the longest side `x`

leaving `x-4` as the height