Essay. Show all work. the rectangular swimming pool is given by 2x^2-5x-3 ft.^2. One side length of the pool is given by 2x+1 feet. What is an algebraic expression for the other side length of the pool? Simplify this, and include correct units as part of your answer.

Answer 1

Area = (2x+1)S = 2x^2 - 5x -3,
S = (2x^2 -5x -3) / (2x+1),
Factor the numerator and get:
S = (x-3)(2x+1) / (2x+1),
S = x - 3. = Expression for other side.

The AC Method was used for factoring:
A*C = 2 * (-3) = -6 = 1*(-6) = 2*(-3).
Select the pair of factors whose sum =
-5:
2x^2 + x-6x - 3 = 0,
Group the 4 terms into 2 factorable pairs:
(2x^2+x) + (-6x-3) = 0,
x(2x+1) - 3(2x+1) = 0,
(2x+1)(x-3) = 0,