Prove the following:
Let f(x) be a polynomial in R[x] of positive degree n.
1. The polynomial f(x) factors in R[x] as the product ofpolynomials of degree
1 or 2.
2. The polynomial f(x) has n roots in C (counting multiplicity).In particular,
there are non-negative integers r and s satisfying r+2s = n suchthat
f(x) has r real roots and s pairs of non-real conjugate complexnumbers as
roots.
3. The polynomial f(x) factors in C[x] as the product of ndegree-one polynomials.
