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Where f(z) is a complex polynomial of degree n, and g(z) is a complex polynomial of degree n-1, and f(q)=0, I can't seem to prove

f(z)=(z-q)g(z)

I have substitituted for each of the polynomials and distributed out the z and q terms, but I am unsure how to manipulate this equation. Help anyone?

I am at the point so far where I have

anz^n + an-1z^n-1 +...+a1z+a0= bn-1z^n +bn-2z^n-1+...b1z^2+b0z-q(bn-1z^n-1+bn-2z^n-2+...b0)

But unable to manipulate this further.

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# Complex Polynomial Theorem

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