Question

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

Answer 1

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 `f(x)=x^3+2x-5x-6`
suggests that the solution set might be `xepsilon{-3,-1,+2}`

We can check this by using these values for a factoring:
`color(white)("XXXXX")` `(x+3)(x+1)(x-2)`

Multiplying these possible factors we find that, in fact,
`color(white)("XXXXX")` `(x+3)(x+1)(x-2) = x^3+2x^2-5x-6`
so
the values previously considered to be merely "possible" have been verified as correct.