math
posted by latesha on .
Use factoring by grouping to solve the following equation.
4x3 + 8x2 − 9x − 18 = 0
x = 1 (smallest value)
x = 2
x = 3 (largest value)

x = 1 is not a solution. You can easily prove that yourself.
When x = 2,
4x^3 + 8x^2 − 9x − 18 = 28
So that is not a solution, either. Neither is x = 3. How did you come up with your answers?
When x = 2,
32 +32 +18 18 = 0
So x+2 is a factor of the polynomial.
The other factor is
(4x^3 + 8x^2 − 9x − 18)/(x+2)
= (4x^2 9) = (2x +3)(2x3)
So the other two solutions are
x = 3/2 and x = 3/2