<s>[INST] If $P(x) = (x^4+x^3-3x^2+4x-4)\cdot q(x) + (2x^3-5x^2+7x-3)$ find $P(2)$ 
If for the polynomial $P(x)$ is true that $$P(x) = (x^4+x^3-3x^2+4x-4)\cdot q(x) + (2x^3-5x^2+7x-3)$$ find $P(2)$

I assumed that the polynomial $(x^4+x^3-3x^2+4x-4)$ has $(x-2)$ as one of its factors, but it turns out that this is not true.
By the equation we got that $P(2)=16\cdot q(2) + 7$ but I don't know what I should do next.
 [/INST] I give you what I think is the only chance that your problem has a meaning. 
There are many possibilities for a such polynomial: you can choose for $g(x)$ any arbitrary polynomial and the resultant one $$P(x) = (x^4+x^3-3x^2+4x-4)\cdot g(x) + (2x^3-5x^2+7x-3)$$ satisfy in fact the property of your statement. 
In particular you can do $P(x)=2x^3-5x^2+7x-3$ so the polynomial is the rest itself in whose case the answer is the constant polynomial $7$.
For this, you have written yourself the general answer, where $g(x)$ is an arbitrary polynomial (if $g$ has $x=2$ as a root then the rest is still $7$ of course).
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