Related To Polynomial Division. Show how a polynomial with odd number of term will never be divisible by a divisor with x+1 as factor for modulo 2 arithmetic.

Brenda Jordan

Brenda Jordan

Answered question

2022-11-02

Related To Polynomial Division. How to prove the following result. Show how a polynomial with odd number of term will never be divisible by a divisor with x + 1 as factor for modulo 2 arithmetic.

Answer & Explanation

Paskcreessy4k5

Paskcreessy4k5

Beginner2022-11-03Added 20 answers

Step 1
In modulo 2 arithmetic (that is in GF(2)) any polynomial will be of the form x a 1 + . . . + x a k , since we omit the terms with zero coefficient.
Saying that x + 1 cannot be a factor of x a 1 + . . . + x a k is the same as saying that -1 (which is equal to 1) is not a root of x a 1 + . . . + x a k .. Obviously in GF(2) 1 is a root of x a 1 + . . . + x a k if and only if k is even.

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