A Concrete Introduction to Higher Algebra pp 531-556 | Cite as

# Factoring in ℤ[*x*]

Chapter

In Section 17D we showed that if *f(x)* is a polynomial with coefficients in ℤ, then one can determine in a finite number of steps the complete factorization of *f(x)* into a product of irreducible polynomials in ℚ[*x*]. The method, Lagrange interpolation, is quite slow in practice.

In this chapter, we'll give another proof of the finiteness of the process of factoring, and then describe some refinements of the proof that speed up the process.

## Keywords

Null Space Great Common Divisor Irreducible Polynomial Monic Polynomial Irreducible Factor
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