The remainder obtained by dividing on
the generator polynomial
is 
Given:
The generator polynomial is 
The polynomial is 
Explanation:
There are two methods of dividing the two polynomials.
(1). Synthetic division
(2). Long division method
The fraction can be expressed as,

The denominator of the fraction is
and the numerator of the fraction is 
Divide
by
to obtain the remainder and the quotient of the polynomial.
The remainder obtained by dividing on
the generator polynomial
is 
Kindly refer the image attached below.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Long division method
Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree, cubic polynomial, quadratic equation.