Let p(x1, x2,…, xn) be a multivariate polynomial in n variables and degree d over a field F such..

Let p(x1, x2,…, xn) be a multivariate polynomial in n variables and degree d over a field F such that p() is not identically 0. Let I _ F be a finite subset. Then the number of elements Y _ I n such that p(Y) = 0 is bounded by |I| n_1 · d. Note that Y is an n tuple. (i) Prove this using induction on n and the fundamental theorem of algebra. (ii) Give an alternate proof of the matrix product verification C = A·B using this result. Hint: What is the degree and the field size in this cas