Ok, I'm trying to teach my kid how to factor polynomials. I already know how to factor bi- and tri- nomials and I already know how to take the GCF (Greatest Common Factor), for instance:

With the equation:

x^3 - 7x^2 - 16x + 112

This can be grouped into (x^3 - 7x^2) - (16x -112)

Then can factor out:

x^2(x - 7) - 16(x - 7)

Which then becomes:

(x^2 - 16)(x - 7)

And finally:

(x - 4)(x + 4)(x - 7)

That's all well and good... but what about something like:

x^3 + 3x^2 - 46x - 168

In this case, if I KNOW any of the factors already, I can determine the rest... but how do I get a factor to begin with? The GFC doesn't seem to work for this...

And, again, I want to point out this is me trying to learn how to teach someone else, not actual homework...

(And to demonstrate that I know the answer):

(x+ 6)(x - 7)(x + 4)

http://mathworld.wolfram.com/NewtonsMethod.html

analytically

http://www.dpmms.cam.ac.uk/~wtg10/cubic.html