# Factoring is important in mathematics

Hi,
Factoring is important in mathematics so I should know how to factor things. But I don't see how one should factor something! I have looked all over the web but I still don't get it. Could someone show me how factoring works? I would appreciate it.

Thank you.

Hurkyl
Staff Emeritus
Gold Member
What sorts of things do you want to factor?

Polynomials.

Hurkyl
Staff Emeritus
Gold Member
To factor an arbitrary polynomial over a finite field, something like Berlekamp's method is usually used.

To factor arbitrary rational polynomials (or polynomials over a number field), I think the favorite method is to use numerical methods to find a root, and the use lattice methods to recover the minimal polynomial of that root.

I mostly want to use factorization because I want to find the critical points of a given function so I can use it to find the maxima and minima of the given function.

To factor an arbitrary polynomial over a finite field, something like Berlekamp's method is usually used.

To factor arbitrary rational polynomials (or polynomials over a number field), I think the favorite method is to use numerical methods to find a root, and the use lattice methods to recover the minimal polynomial of that root.
I'm sorry, but I don't understand this. Could you explain this like you would explain a 14-year old (like me)? I'm sorry for my ignorance.

Hurkyl
Staff Emeritus
Gold Member
Oh, if you're trying to factor small polynomials by hand, the rational root theorem is one of the most useful techniques.

The thing I mentioned is more of a sledgehammer approach that a computer would use to factor a large polynomial.

matt grime