Answer: To find the solutions for the function f(x) = 2x^3 + 5x^2 + 5x + 6, where f(-2) = 0, we need to substitute -2 for x in the function and set it equal to 0:
f(-2) = 2(-2)^3 + 5(-2)^2 + 5(-2) + 6 = 0
Simplifying this equation, we get:
8 - 20 - 10 + 6 = 0
We then proceed to factor the polynomial:
2x^3 + 5x^2 + 5x + 6 = (2x + 3)(x+1)(x+2) = 0
To find the solutions of this equation, we set each factor equal to zero and solve for x:
2x + 3 = 0 => x = -3/2
x + 1 = 0 => x = -1
x + 2 = 0 => x = -2
So the solutions for the function f(x) = 2x^3 + 5x^2 + 5x + 6, where f(-2) = 0, are x = -3/2, x = -1 and x = -2
Explanation: