Is it possible to find polynomials with rational coefficients P ( x ) , Q...

Joglxym

Joglxym

Answered

2022-11-23

Is it possible to find polynomials with rational coefficients P ( x ) , Q ( x ) such that P x 3 + P x 2 + Q x + 2 Q = 1 ?

Answer & Explanation

lelestalis80d

lelestalis80d

Expert

2022-11-24Added 23 answers

Write the equation as
P ( x 3 + x 2 ) + Q ( x + 2 ) = 1.
Since gcd ( x 3 + x 2 , x + 2 ) = 1 over Q the solution exists and can be found by employing the Euclidean algorithm.

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