Chapter 7 Polynomials

In this chapter we change direction altogether (or at least it will seem so to begin with). We shall work in $\mathbb{R}$ throughout. Our aim is to generalize the notion of a highest common factor from pairs of (non-zero) integers to pairs of (non-zero, real) polynomials and then develop a counterpart of the Euclidean algorithm which will enable us to calculate such highest common factors.