Find the gcd of the given polynomials f (x) and g(x) over the specified coefficient ring R and express it as an R[x]-linear combination of f (x) and g(x). (a) f (x) = x4 − x3 − x2 + 1 and g(x) = x3 − 1 over Q. (b) f (x) = x4 + 3x3 + 2x + 4 and g(x) = x2 − 1 over Z5. (c) f (x) = x3 − 2x2 + 1 and g(x) = x2 − x − 3 over Q.
Find the gcd of the given polynomials f (x) and g(x) over the specified coefficient ring R and express it as an R[x]-linear combination of f (x) and g(x). (a) f (x) = x4 − x3 − x2 + 1 and g(x) = x3 − 1 over Q. (b) f (x) = x4 + 3x3 + 2x + 4 and g(x) = x2 − 1 over Z5. (c) f (x) = x3 − 2x2 + 1 and g(x) = x2 − x − 3 over Q.
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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Find the gcd of the given polynomials f (x) and g(x) over the specified coefficient ring R and
express it as an R[x]-linear combination of f (x) and g(x).
(a) f (x) = x4 − x3 − x2 + 1 and g(x) = x3 − 1 over Q.
(b) f (x) = x4 + 3x3 + 2x + 4 and g(x) = x2 − 1 over Z5.
(c) f (x) = x3 − 2x2 + 1 and g(x) = x2 − x − 3 over Q.
express it as an R[x]-linear combination of f (x) and g(x).
(a) f (x) = x4 − x3 − x2 + 1 and g(x) = x3 − 1 over Q.
(b) f (x) = x4 + 3x3 + 2x + 4 and g(x) = x2 − 1 over Z5.
(c) f (x) = x3 − 2x2 + 1 and g(x) = x2 − x − 3 over Q.
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