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According to the Fundamental Theorem of Algebra, every nonconstant polynomial f (x) ∈ C[x] with complex coefficients...

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Advance Math

According to the Fundamental Theorem of Algebra, everynonconstant polynomial f (x) ∈

C[x] with complex coefficients has a complex root.

  1. (a) Prove every nonconstant polynomial with complex coefficientsis a product of linear polynomials.

  2. (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.

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