Question 4 (Essay Worth 10 points) (06.03,06.04 MC) 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 10x^2-6x The width of 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:<br />To find the expression for the length of the rectangular space, we can use the formula for the area of a rectangle, which is length times width. We are given that the area is represented by the expression $10x^{2}-6x$ and the width is represented by the expression $2x$. <br /><br />Let's denote the length as $L$. Then, we have:<br /><br />Area = Length * Width<br />$10x^{2}-6x = L * 2x$<br /><br />To solve for $L$, we divide both sides of the equation by $2x$:<br /><br />$L = \frac{10x^{2}-6x}{2x}$<br /><br />Simplifying the expression, we get:<br /><br />$L = 5x - 3$<br /><br />So, the expression to represent the length of the rectangular space is $5x - 3$.<br /><br />Part B:<br />To prove that our answer in Part A is correct, we can multiply the length and the width of the rectangle and check if it equals the given area expression.<br /><br />Length * Width = $(5x - 3) * 2x$<br /><br />Expanding the expression, we get:<br /><br />$10x^2 - 6x$<br /><br />Since this expression matches the given area expression, we can conclude that our answer in Part A is correct.