Find the gcd of the given polynomials f(x) and g(x) over the specified coefficient ring R...

 

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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[r]-linear combination of f(x) and g(x). (a) f(x) =x²-x³x² + 1 and g(x)= x³ - 1 over Q. (b) f(x) = x² + 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[r]-linear combination of f(x) and g(x). (a) f(x) =x²-x³x² + 1 and g(x)= x³ - 1 over Q. (b) f(x) = x² + 3x³ + 2x + 4 and g(x) = x² - 1 over Z5. (c) f(x) = x³ - 2x² + 1 and g(x)=x²-x-3 over Q. .

Answer rating: 100% (QA)

a fx x 1 gx x 1 since gx degree is less than fx degree then z 1x 1x2 x x ... View the full answer