r(x)Find polynomials q(x) and r(x) such that a(x) = b(x)q(x) +r(x) and0 or has smaller degree than b(x) for each of the following:+ 3x + 1 and b(x)=x² + x + 1 in Q[x]A. a(x) = 3x¹ − 2x³B. a(x) = x² + 7xC. a(x) = 2x¹ + x²=3 and b(x) = 2x² + 1 in Q[x]x + 1 and b(x) = 2x + 1 in Z5 [x]D. a(x) = 3x² + 2x³ - x² – 3x 2 and b(x) = 3x² + 2 in Z7 [x]

Answered: r(x) Find polynomials q(x) and r(x)…

r(x) Find polynomials q(x) and r(x) such that a(x) = b(x)q(x) +r(x) and 0 or has smaller degree than b(x) for each of the following: A. a(x) = 3x¹ — 2x³ + 3x + 1 and b(x) = x² + x + 1 in Q[x] =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

r(x)
Find polynomials q(x) and r(x) such that a(x) = b(x)q(x) +r(x) and
0 or has smaller degree than b(x) for each of the following:
+ 3x + 1 and b(x)
=
x² + x + 1 in Q[x]
A. a(x) = 3x¹ − 2x³
B. a(x) = x² + 7x
C. a(x) = 2x¹ + x²
=
3 and b(x) = 2x² + 1 in Q[x]
x + 1 and b(x) = 2x + 1 in Z5 [x]
D. a(x) = 3x² + 2x³ - x² – 3x 2 and b(x) = 3x² + 2 in Z7 [x]

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