Final answer:
To find the x-intercepts for the function g(x) = x^3 + x^2 - 6x, you factor the equation and solve for x, which yields the intercepts at 0, 2, and -3.
Step-by-step explanation:
The x-intercepts of a function are the values of x at which the function equals zero. To find the x-intercepts for the function g(x) = x^3 + x^2 - 6x, we need to set the function equal to zero and solve for x:
g(x) = 0
x^3 + x^2 - 6x = 0
First, factor out an x:
x(x^2 + x - 6) = 0
Now, factor the quadratic:
x(x - 2)(x + 3) = 0
Setting each factor equal to zero gives us the x-intercepts:
Therefore, the x-intercepts of the function g(x) are 0, 2, and -3.