The width w of a rectangular swimming pool is x + 4. The area A of the pool is x^3 - 13x + 12. What is an expression for the length of the pool?
(1 point)
A. x^2 + 4x + 3
B. x^2 - 4x - 3
C. x^2 - 4x + 3
D. x^2 + 4x - 3
To find the length of the pool, we can use the formula for the area of a rectangle: A = length * width.
Given that the width w of the pool is x + 4, we can set up the equation A = (x+4) * length.
Plugging in the given area A = x^3 - 13x + 12, we get:
x^3 - 13x + 12 = (x+4) * length.
To find the length, we can divide both sides of the equation by (x+4):
length = (x^3 - 13x + 12) / (x+4).
Factoring the numerator, we get:
length = [(x-1)(x^2 + x - 12)] / (x+4).
Simplifying the expression, we get:
length = (x-1)(x+3)(x-4) / (x+4).
Therefore, the expression for the length of the pool is:
length = (x-1)(x+3)(x-4) / (x+4).
None of the provided options match this expression, so the correct answer is None of the above.