Thanks Consider the polynomial x^ 5 + 6x^ 3+ 9x+ 15 in Q[x] and let a be root in

Question

Thanks

Consider the polynomial x^ 5 + 6x^ 3+ 9x+ 15 in Q[x] and let a be root in some extension field of Q. Compute the following: A. (a^4 + 2a^ 3 -a + 3) (a^ 3 + 2a~2 -1) (note: I think the answer is -26a^ 4 + 2a^ 3 - 45a^ 2 - 41a +27) please check. Not sure on B: (a ^ 4 + 2a ^ 3 - a +3 ) / (a ^ 3 +2a ^ 2-1 ) Note- to compute an inverse of an element, think of modular arithmetic, when we want to compute a ^-1 mod n we use the Euclidean algorithm to find x, y in Z such that ax + ny=l then x=a ^ -l mod n In this case you want to compute (a ^ 3 +2a ^ 2 -1)^-1 mod (a ^ 5 +6a ^ 3 +9a +15)

Explanation / Answer

a is correct

b is -2a+3a^2+4

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