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For questions related to divisors in the sense of algebraic geometry (Cartier divisors, Weil divisors and so on). For question on divisors in the number theoretic sense please use the tag divisors-multiples.

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What are conditions such that the polynomial $x^2+1$ divides $p(y)+q(z)+ax+b=F(x,\, y, \,z)$? [closed]

I came across the following problem: What are conditions such that the polynomial $x^2+1$ divides $p(y)+q(z)+ax+b=F(x,\,y,\,z)$,? Here $p$ and $q$ are also polynomials and $a$, $b$ are real numbers …
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