Letf(x)∈f[x] be a polynomial of degree n≥1 and let bars denote passage to the quotient f[x]/(f(

prove that for each g(x) there is a unique polynomial g0(x)of degree≤n−1 such that g(x) =g0(x) (equivalently, the elements1,x, . . ,xn−1are a basis of the vector spacef[x]/(f(x)) overf).

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