Question

A pencil holder is in the shape of a rectangular prism. The volume of a pencil holder is represented by 8x^3 +4x^2-84x. Find the possible dimensions of the pencil holder if the dimensions are represented by polynomials with integer coefficients.

Answer 1

4x, 2x+7 and x-3.

Explanation:

The volume of the rectangular prism shaped pencil holder is given as:

`8x^3 +4x^2-84x`

To determine the dimensions of the pencil holder, we factorize the given expression.

`8x^3 +4x^2-84x\\=4x(2x^2+x-21)\\=4x(2x^2+7x-6x-21)\\=4x(2x^2-6x+7x-21)\\=4x(2x(x-3)+7(x-3))\\=4x(2x+7)(x-3)`

Therefore, the possible dimensions of the pencil holder are:

4x, 2x+7 and x-3.