Let be a polynomial with real coefficients such that for all Prove that there exists a positive integer n such that is a polynomial with nonnegative coefficients.
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Let $P(x)$ be a polynomial with real coefficients such that $P(x) > 0$ for all $x \geq 0.$ Prove that there exists a positive integer n such that $(1 + x)^n \cdot P(x)$ is a polynomial with nonnegative coefficients.
Izvor: Međunarodna matematička olimpijada, shortlist 1997
Školjka 
be a polynomial with real coefficients such that 
for all 
Prove that there exists a positive integer n such that 
is a polynomial with nonnegative coefficients.