<s>[INST] How to compute remainder of division of $P(x)$ by $x^2 -3x+2$? 
The remainder of division of $P(x)$ by $x^2−1$ is $2x+1$, and the remainder of division of the same polynomial by $x^2−4$ is $x+4$. Compute the remainder of division of $P(x)$ by $x^2−3x+2$.

I will translate these into math equations
$$P(x) = (x^2-1)Q(x)+ 2x+1$$
$$P(x) = (x^2 -4)R(x)+x+4$$
And let 
$$f(x) = P(x) $$
We're asked to find the remainder when this polynomial is divided by $x^2 -3x+2$. So, there are two equations, which is why I'm confused with what to use in the equation $f(x) = P(x)$. What am I missing here?
Regards
 [/INST] $P(x)=(x^2-1)Q(x)+2x+1;$
$P(x)=(x^2-4)R(x)+x+4;$
$P(x)=(x-1)(x-2)S(x)+ax+b.$
1)$P(1)=2(1)+1=a+b;$
2)$P(2)=2+4=2a+b;$
$3=a+b$; and $6=2a+b;$
$a=3$; $b=0;$
Remainder: $ax+b=3x.$
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