solve the polynomial inequality and graph the solution set on a real number line. set in interval notation.

Question

x^3+2x^2-4x-8>0

I have been staring at this problem for the last 15 minutes because I just don't understand it, somebody please help me?

Answer 1

x^3+2x^2-4x-8 > 0
(x+2)^2 (x-2) > 0

Now, you know that the graph touches the x-axis at x = -2 and cross it at x=2

Since y<0 for large x<0, that means that y<0 for x < -2, and stays <0 up to x=2, where it crosses the x-axis.

So, the solution set is x>2