2. (Theorem 20.5) Let f(0) = 20 +22+ +0.7." € F[u], where F is a field. We can define the derivative of f(), denoted by

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2 Theorem 20 5 Let F 0 20 22 0 7 F U Where F Is A Field We Can Define The Derivative Of F Denoted By 1 (21.68 KiB) Viewed 18 times

2. (Theorem 20.5) Let f(0) = 20 +22+ +0.7." € F, where F is a field. We can define the derivative of f(), denoted by f'(x), as f'(x) = a1 +2a22+...+nana" 1. Show that f(:) has a multiple zero (a zero with multiplicity greater than 1) in some extension E if and only if f() and f'(2) have a common factor of positive degree in F2 a