Proof: A (real) polynomial of degree d has at most d (real) roots

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A (real) polynomial of degree $d$ has at most $d$ (real) roots

The catch is the only things I can cite are

1) The Division Algorithm for Polynomials

2) Prop 6.19: Let p(x) be a real polynomial. The number z is a root of p(x) iff there exists polynomial q(x) such that p(x)=(x-z)q(x).

Any help appreciated.