product of polynomials has only positive coefficients

Question

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!

score 2 · Accepted Answer · answered Nov 29 '16 at 02:26

2

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

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

answered Nov 29 '16 at 02:26

dxiv

1 Answers1