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Complex Polynomial Proof : Factoring

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1. Consider the complex polynomial of degree n
p(z) = zn + a1zn-1 + ... + an-1z +an
show that if z1 is a zero then p(z) = (z - z1)q(z), where q is a polynomial of degree n-1 (Hint: consider p(z) = p(z) - p(z1)). Argue further that p can be fully factored like
p(z) = (z - z1)...(z - zn)

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A proof is provided for factoring of a complex polynomial.

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1. Consider the complex polynomial of degree n
p(z) = zn + a1zn-1 + ... + an-1z +an
show that if z1 is a zero then p(z) = (z - z1)q(z), where q is a polynomial of degree n-1 (Hint: consider p(z) = p(z) - p(z1)). Argue further that p can be fully factored like
p(z) = (z - z1)...(z - ...

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