Question

The area of a rectangle is (x4 + 4x3 + 3x2 – 4x – 4), and the length of the rectangle is (x3 + 5x2 + 8x + 4). If area = length × width, what is the width of the rectangle

Answer 1

length x width = area

-> width = area / length
= (x^4 + 4x^3 + 3x^2 - 4x - 4) / (x^3 + 5x^2 + 8x +4)
= (x+2)^2*(x-1)(x+1) / (x+2)^2*(x+1)
= x-1

-> width = x-1

Answer 2

`x-1`

Explanation:

Given : The area of a rectangle is
`x^4 + 4x^3 + 3x^2-4x - 4`.

Length of rectangle =
`x^3 + 5x^2 + 8x + 4`

To Find: Width of rectangle

Solution:

Area of rectangle =
`Length * width`

Substituting the values:

`x^4 + 4x^3 + 3x^2-4x - 4=(x^3 + 5x^2 + 8x + 4) * Width`

`(x^4 + 4x^3 + 3x^2-4x - 4)/(x^3 + 5x^2 + 8x + 4)=Width`

`x-1=Width`

Thus the width of the given rectangle is
`x-1`