Theorem. Let F be a field and ƒ € F[x] a polynomial of degree n. Then there is a finite-dimensional extension of F in which f factors into linear factors f(x) = (x – a1) · … · (x – a,n). Proof. Apply the last theorem repeatedly to get getting extensions of extensions and factor out a linear factor each time until the degree is reduced to 1.

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A: We will use repeated differentiation to prove this

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Q: Part A: Identify the zeros of the following polynomial function: f(x) = -x(x + 2)(x – 2)(x + 1)

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