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The factor $x−a_j$ is omitted, so $f_j$ has degree n-1

a) Prove that the set $f_1(x),...,f_n(x)$ is a basis of the vector space of all polynomials of degree ≤ n - 1 in x with coefficients in F.

b) Let $b_1,...,b_n$ in F be arbitrary (not necessarily distinct). Prove that there exists a unique polynomial g(x) of degree ≤ n - 1 in x with coefficients in F.

I don't know how to go about this question. Any help would be appreciated.