Im looking for an example of two polynomials with integer coefficients in one variable with:

1) both have positive "constant"-coefficient

2) atleast one of the coefficients of atleast one of the two polynomials is negative

3) their product has only positive coefficients

It seems simple to find an example, but I couldn't think of one!


Hint: $\;(x+1)\,(x^2-x+1)\;=\;\cdots$

Or, in general: $\;(x+1)\,(x^{2n}-x^{2n-1} + x^{2n-2} - \cdots + x^2 - x +1)=\;\cdots\;$


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