According to the Fundamental Theorem of Algebra, everynonconstant polynomial f (x) ∈
C[x] with complex coefficients has a complex root.
(a) Prove every nonconstant polynomial with complex coefficientsis a product of linear polynomials.
(b) Use the result of the previous exercise to prove everynonconstant polynomial with real coefficients is a product oflinear and quadratic polynomials with real coefficients.
