Consider a polynomial $P(x) = x^4+x^3-3x^2+x+2$. Prove that at least one of the coefficients of $(P(x))^k$, ($k$ is any positive integer) is negative. (5)
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Tags: polynomial, algebra
Consider a polynomial $P(x) = x^4+x^3-3x^2+x+2$. Prove that at least one of the coefficients of $(P(x))^k$, ($k$ is any positive integer) is negative. (5)