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Find-polynomial-u-v-Q-x-such-that-x-4-1-u-x-x-7-1-v-x-x-1-

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Question Number 179327 by greougoury555 last updated on 28/Oct/22
Find polynomial u,v ∈Q[x] such that (x^4 −1)u(x)+(x^7 −1)v(x)=(x−1)
Findpolynomialu,v∈Q[x]suchthat(x4−1)u(x)+(x7−1)v(x)=(x−1)
Answered by manxsol last updated on 28/Oct/22
(x−1)(x^3 +x^2 +x+1)u(x)+(x−1)(x^6 +x^5 +x^4 +x^3 +x^2 +x+1)v(x)=x−1 then u(x)=(1/(2(x^3 +x^2 +x+1))) v(x)=(1/(2(x^6 +x^5 +x^4 +x^3 +x^2 +x+1)))
(x−1)(x3+x2+x+1)u(x)+(x−1)(x6+x5+x4+x3+x2+x+1)v(x)=x−1thenu(x)=12(x3+x2+x+1)v(x)=12(x6+x5+x4+x3+x2+x+1)

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