Question

The area of a rectangular swimming pool is 18x^2-9x-5. The length of the pool is 6x+5. What is the width of the pool?

Answer 1

(3x + 1)

Explanation:

Factor the trinomial f(x) by the new AC Method (Socratic Search):
`f(x) = 18x^2 - 9x - 5 =` 18(x + p)(x + q)
Converted trinomial:
`f'(x) = x^2 - 9x - 90 =` (x + p')(x + q')
Find p' and q' knowing the sum (-9) and the product (-90).
They are: p' = - 15 and q' = 6.
Back to f(x) --> `p = (p')/a = - 15/18 = - 5/6`, and `q = (q')/a = 6/18 = 1/3`.
Factored form
`f(x) = 18(x - 5/6)(x + 1/3) = (6x - 5)(3x + 1)`.
The pool 's width is (3x + 1)