Can you please answer each part of this question correctly. Thank you This question concerns the field GF(16). The modulus is P(x) = x² + x + 1.Please answer the following questions about arithmetic in this field.a) If p(x) = x² + x, what is p¯¹(x) modulo P?b) lf p(x) = x³ + x² + x, what is p¯¹(x) modulo P?c) If p(x) = x + 1, what is p¹(x) modulo P?d) If p(x) = x² + x + 1, what is p¯¹(x) modulo P?Hint: The inverse of each polynomial appears in another sub-part of the question

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 6TFE

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Please answer the following questions about arithmetic in this fiel a) If p(x) = x² + x, what is p¹(x) modulo P? b) If p(x) = x³ + x² + x, what is p-¹(x) modulo P? c) If p(x) = x + 1, what is p¹(x) modulo P? d) lf p(x) = x² + x + 1, what is p¯¹(x) modulo P?