Steven Weintraub's book {\em A Guide to Advanced Linear Algebra} includes the following remark:

"Of course, there is no algorithm for factoring polynomials, as we know from Galois theory."

I can't make sense of this. I feel confident that Galois theory doesn't speak to the question of algorithms, and confident that there do exist algorithms for factoring integer polynomials over the integers (after Kronecker), and strategies for computing in the field of algebraic numbers that make tautological the question of factoring polynomials irreducible over the rationals.

Have I missed some way to salvage this remark?