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

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

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

(a) Prove every nonconstant polynomial with complex coefficients is a product of linear polynomials.
(b) Use the result of the previous exercise to prove every nonconstant polynomial with real coefficients is a product of linear and quadratic polynomials with real coefficients.

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Expert Solution

Colby Messinger answered 1 year ago

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