First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x x^3+2x^2-8x=0 x(x^2+2x-8)=0 x(x+4)(x-2)=0 x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative. Plugging in a -5 gets us -35 -1 gets us 9 1 gets us -5 3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
To solve this, we following the same steps as when solving inequalities. We just have to remember to reverse the sign if we multiply or divide by a negative number.
