Question

The area of a rectangle is (x^3-5x^2+3x-15), and the width of the rectangle is (x^2+3). If area = length × width, what is the length of the rectangle?

a) (x^2 - 8x + 5)
b) (x^2 - 8x - 5)
c) (x^2 + 8x + 5)
d) (x^2 + 8x - 5)

Answer 1

To find the length of the rectangle, divide the area polynomial by the width polynomial, which yields the length as x^2 - 8x + 5.

Step-by-step explanation:

The question asks us to find the length of a rectangle given its area expressed as a polynomial (x3 - 5x2 + 3x - 15) and its width as another polynomial (x2 + 3). We know that area of a rectangle is calculated by multiplying its length by its width. Therefore, to find the length, we must divide the area by the width.

Dividing the area polynomial by the width polynomial, we get:


((x3 - 5x2 + 3x - 15) / (x2 + 3)) = x - 8x + 5

Hence, the correct answer for the length of the rectangle is option (a) x2 - 8x + 5.