- #1

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I have the graph of [tex]f(x)=x^{3}+3x^{2}-9x+3[/tex]. I know the x intercepts of the function from looking at the graph, what I want to know is how to factor the equation by hand to derive those intercepts.

[tex]x(x^{2}+3x^{2}-9)=-3[/tex] doesn't help because factoring the quadratic in the middle gives me the zeros of that particular piece, which are meaningless, because I'm not looking for those zeros. I've tried factoring by pieces, but I can't get the right products to pop out.

Surely, because the graph exists at all, and because the function is continuous across the x-axis, then there must be a way to factor the zeros out of [tex]f(x)[/tex]? Or am I totally off base with that assumption?