Final answer:
To determine the length of a rectangular swimming pool, substitute x with 24 in the given perimeter polynomial, then use the perimeter formula to solve for the length.
Step-by-step explanation:
The student has asked to find the length of a rectangular swimming pool given the perimeter is expressed as a cubic polynomial in terms of x, (x³ - 23x² - 17x + 2) feet, and the width is given as x feet. To find the length when the width is 24 feet, we substitute x with 24 in the polynomial and use the perimeter formula of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
First, we express the perimeter polynomial with x = 24: (24³ - 23(24)² - 17(24) + 2).
Next, calculate the value of the expression:
P = 24³ - 23(24)² - 17(24) + 2.
After finding the value of the perimeter, we use the formula to solve for the length (l):
2l + 2(24) = P.
Simplify and solve for l to find the length of the pool.