Question

The area A of a rectangle with a width of x−2 is given by A=x^4+2x^3−16x^2+32. Find an expression for the length of the rectangle. Please show work.

a) A = x^4 + 2x^3 - 16x^2 + 32

b) A = x^3 - 2x^2 + 32

c) A = x^2 + 2x - 16

d) A = x^2 - 2x + 32

Answer 1

To find the length of the rectangle, divide the given area by the width, which results in the expression for the length being x^3 - 2x^2 + 32.

Step-by-step explanation:

The area A of a rectangle is given by the formula A = length × width. In this case, the width is given as x - 2, and the area A is provided as x^4 + 2x^3 - 16x^2 + 32. To find the expression for the length of the rectangle, we divide the area by the width. Performing the division yields:

• A = x^4 + 2x^3 - 16x^2 + 32
• Width = x - 2

So, the length is:

Length = A / Width = (x^4 + 2x^3 - 16x^2 + 32) / (x - 2)

When we perform the division, we find the length expression to be:

b) A = x^3 - 2x^2 + 32