$y_2\left(x\right)=0$ , $y_1\left(x\right)=1$ ,

$q\left(x\right)=x^2+1$ , $r\left(x\right)=x^2$ ,

$y\left(x\right)=x^2+1$ , $y_2\left(x\right)=1$ , $y_1\left(x\right)=x^2+1$ ,

$P\left(x\right)=x^6+x^4+x+1$ , $A\left(x\right)=x^2$ .