For polynomial arithmetic with coefficients in Z_{11}, perform the followi

Weltideepq

Weltideepq

Answered question

2021-11-06

For polynomial arithmetic with coefficients in Z11, perform the following calculations.
a. (x2+2x+9)(x3+11x2+x+7)
b.(8x2+3x+2)(5x2+6)

Answer & Explanation

Todd Williams

Todd Williams

Beginner2021-11-07Added 18 answers

a.
(x2+2x+9)(x3+11x2+x+7)
=x5+11x4+x3+7x2+2x4+22x3+2x2+14x+9x3+99x2+9x+63
=x5+13x4+32x3+108x2+23x+63
In coefficients Z11
=x5+2x4+10x3+9x2+x+8
[oti:-1\%11=1, 13\%11=2, 32\%11=10, 108\%11=9, 23\%11=1, 63\%11=8\rightoti:1%11=1,13%11=2,32%11=10,108%11=9,23%11=1,63%11=8]
b.
(8x2+3x+2)(5x2+6)
=40x4+58x2+15x3+18x+12
InZ11 coefficients,
=7x4+4x3+3x2+7x+1
[oti:-40\%11=7, 58\%11=3, 15\%11=4, 18\%11=7, 12\%11=1\rightoti:40%11=7,58%11=3,15%11=4,18%11=7,12%11=1]

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