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Consider the following two polynomials in F17[x]
(a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials.
(b) Use the FFT algorithm, by hand, to multiply these two polynomials.
Remember that if a polynomial has degree 3 or less then it is irreducible if and only if it has at least one linear factor, that (x - a) is a linear factor of a polynomial f(x) if and only if f(a) = 0 and that for small elds it is easy to check by hand if a particular value is a root of a polynomial.
(a) Which of the following polynomials are reducible and irreducible in F5[x]? What is the factorization of the reducible ones?
(b) Does the following system have a unique solution of smallest degree:
Given two functions f(x) and g(x) which are differentiable on some interval I (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int
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Here we look at only the rules without going into their proofs. They are: a 0. If a If a If a
13 1/4 34 56/89
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