You have a rectangular space where you plan to create an obstacle course for an animal. The area of the rectangular space is represented by the expression 6x2 − 16x. The width of the rectangular space is represented by the expression 2x. Part A: Write an expression to represent the length of the rectangular space. Then simplify your expression. Show all your work. (6 points) Part B: Prove that your answer in part A is correct by multiplying the length and the width of the rectangle. Show all your work. (4 points)

**Part A:** The expression for the length of the rectangular space is: \frac{6x^2 - 16x}{2x} To simplify this expression, we can factor out 2x from the numerator and cancel it with the denominator. We get: \frac{2x(3x - 8)}{2x} 3x - 8 Therefore, the simplified expression for the length of the rectangular space is: 3x - 8 **Part B:** To prove that our answer in part A is correct, we need to multiply the length and the width and check if we get the same expression as the area. Using the expressions we found, we have: (3x - 8)(2x) To multiply these expressions, we need to use the distributive property. We get: 6x^2 - 16x - 16x + 64 To simplify this expression, we can combine the like terms. We get: 6x^2 - 32x + 64 This is the same expression as the area, so we have proved that our answer in part A is correct.