SOLUTION: consider the integral expression in x! {{{P=x^3+x^2+ax+1}}} where a is rational number at a=[A], the value of P is a rational number for any x which satisfies the equation {{{

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: consider the integral expression in x! {{{P=x^3+x^2+ax+1}}} where a is rational number at a=[A], the value of P is a rational number for any x which satisfies the equation {{{      Log On


   

Question 750022: consider the integral expression in x!
P=x%5E3%2Bx%5E2%2Bax%2B1
where a is rational number
at a=[A], the value of P is a rational number for any x which satisfies the equation x%5E2%2B2x-2=0,and this case the value of P is [B}
solve for A and B
please, im stuck here

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
P=x%5E3%2Bx%5E2%2Bax%2B1
Dividing by x%5E2%2B2x-2 we get x-1 for quotient with -1 for a remainder.
P%28x%29=x%5E3%2Bx%5E2%2Bax%2B1=%28x-1%29%28x%5E2%2B2x-2%29-1=x%5E3%2Bx%5E2-4x%2B1
So A=-4

For any x which satisfies the equation x%5E2%2B2x-2=0,
P%28x%29=%28x-1%29%2A0-1=0-1=-1
so B=-1