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 x width, what is the length

of the rectangle

(x - 5)

Step-by-step explanation:

The area expression can be factored by grouping:

x^3 - 5x^2 + 3x - 15

= (x^3 - 5x^2) + (3x - 15)

= x^2 (x - 5) + 3 (x - 5)

= (x^2 + 3) (x - 5)

We recognize the first of these factors as the given width. Then the other factor must be the length.

The length of the rectangle is (x - 5).