I'm trying to understand what is meant in this paragraph: of "Conics and Cubics. A Concrete Introduction to Algebraic Curves (by Robert Byx)":
He wants to prove that the polynomial $X^2+Y^2-1$ is irreducible using geometrical tools. I have the following doubts:
What he means by Since every line has at least three points on it ?
Why the fact that $X^2+Y^2-1=F(X,Y)\cdot G(X,Y)$, where F, G are lines implies that the circle $X^2+Y^2-1=0$ is made up of two lines?
I would really grateful if anyone could help me.