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)
(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)