Question

How do you factor and solve `3x^3 + 4x^2 - 15x = 0`?

Answer 1

`x = 0, x = 5/3, x = -3`

Explanation:

`f(x) = xy = x(3x^2 + 4x - 15) = 0`.
Factor y by using the new AC Method (Socratic Search)
Converted trinomial: `y' = x^2 + 4x - 45`.
Find p' and q' that have opposite signs (ac < 0), and that has their
sum (b = 4) and their product (c = -45).
They are; p' = -5 and q' = 9.Back to trinomial y, `p = (p')/a = -5/3 = -5/3`, and `q = (q')/a = 9/3 = 3`
Factored form of y:
`y = 3(x - 5/3)(x + 3) = (3x - 5)(x + 3).`
Finally, the real roots of f(x) = x(3x - 5)(x + 3) are:
`x = 0, x = 5/3, and x = -3`