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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:
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If α, β are the zeros of the polynomial x 2 +8x +6 frame a Quadratic polynomial whose zeros are a) 1/α and 1/β b) 1+ β/α , 1+ α/β. Ans. P(x) = x 2 +8x +6 α + β = -8
round to the nearest hundreths 1677.76
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