# How do you find all zeros of #f(x) = x^3 + 2x^2 - 5x - 6#?

##### 1 Answer

Jun 1, 2015

With no immediately obvious solutions, one way to attempt this is to plot the graph of the function.

Note that this does not guarantee that the x-intercepts will be exactly as they seem but it gives us some values to consider.

graph{x^3+2x^2-5x-6 [-10, 10, -5, 5]}

The graph of

suggests that the solution set **might** be

We can check this by using these values for a factoring:

Multiplying these possible factors we find that, in fact,

so

the values previously considered to be merely "possible" have been verified as correct.