Find polynomial with given residues modulo two other polynomials
Find a polynomial f(x) of degree 3, which when divided by x^2 - 4, gives a remainder 2x - 5, and divided by x^2 + x + 3 gives a remainder -5x - 9.
Is your question related to SageMath? Do you know about the Chinese Remainder Theorem?
May i suggest a change in the title of the question? i think it should contain a fast description of the problem, like "find a polynomial, given some residues".