Find the value of the real parameters a,b, if there exists a P(X) binomial and the following is true

Question

Find the value of the real parameters a,b, if there exists a P(X) binomial and the following is true

$(X^3-aX^2-bX+1) : P(X) = X^2-X+1 $

I tried to divide and to equalize the remainder to zero, but I think i'm missing something.

Answer 1

Hint: Factorise $x^3+1$ and compare.

Answer 2

you can make a polynomial division like this: $(X^3-aX^2-bX+1):(X^2-X+1)=P(X)$

It´s just a transformation of the origininal equation. Then compare the values of the parameters.

greetings,

calculus.