I'm reading Elementary Algebra by Rouse W. W. Ball, and factorization strategies for quadratics are being discussed.
In the book, we are trying to factor $x^2+2x-1$, so we complete the square
$$x^2+2x-1$$ $$=(x^2+2x+1)-1-1$$ $$=(x+1)^2-2$$
But the author doesn't stop there; he says that we can use difference of squares to factor this further.
$$a^2-b^2=(a+b)(a-b)$$ And thus our equation becomes $$(x+1-\sqrt2)(x+1+\sqrt2)$$
But what bothers me is that the author then says: "These factors are rational so far as $x$ is concerned." I have no idea what this means.
Aren't these factors irrational since $\sqrt2$ is involved?