Factor to find all x-intercepts of the function
f(x)= -x^3-3x^2+10x
To find the x-intercepts of the function, we need to set f(x) equal to zero and solve for x.
Setting f(x) to zero, we have:
0 = -x^3 - 3x^2 + 10x
Let's factor out an x to simplify the equation:
0 = x(-x^2 - 3x + 10)
Now, let's factor the quadratic expression inside the parentheses:
0 = x(-x - 2)(x + 5)
This gives us three potential x-intercepts: x = 0, x = -2, and x = -5.
Therefore, the x-intercepts of the function are 0, -2, and -5.