CS 70 Discrete Mathematics and Probability Theory Fall 2021
1 Polynomial Practice
(a) If f and g are non-zero real polynomials, how many roots do the following polynomials have at least? How many can they have at most? (Your answer may depend on the degrees of f and g.)
(i) f+g (ii) f·g
(iii) f/g,assumingthatf/gisapolynomial
(b) Now let f and g be polynomials over GF(p).
(i) We say a polynomial f = 0 if ∀x, f (x) = 0. If f · g = 0, is it true that either f = 0 or g = 0?
(ii) Howmany f ofdegreeexactlyd