Question

The volume of a rectangular prism is

represented by the expression x3 + 5x2 - 8x -
48 If the length is (x – 3) and the height and
width are equal, what is the width of the prism?
(x + 4)
(x-4)
(x - 2)
(x + 2)
plsss hurry

Answer 1

`x+4`

Explanation:

This question is essentially asking:
`p(x)^2*(x-3)=x^3+5x^2-8x-48`. Find
`p(x)`.

The left hand side can be factored into
`(x-3)(x+4)^2` by the rational root theorem and polynomial division.

We can then divide both sides of the equation to get
`p(x)^2=(x+4)^2`.

Finally, we take the square root of both sides to obtain
`p(x)=x+4`.

So, the answer is
`\boxed{x+4}`