The area of a rectangle is (x3 – 5x2 + 3x – 15), and the width of the rectangle is (x2 + 3). if area = length × 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)

The area expression is the product of (x^2 +3) and (x -5). If the factor (x^2 +3) represents the width of the rectangle, then (x -5) can represent the length.

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

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )