Tessellate S.T.E.M.S - Mathematics - School - Set 1 - Problem 2

Algebra Level 2

You are allowed to do two operations to a quadratic polynomial with integer coefficients. You can either replace \(f(x)\) by \(f(x+a)\) for any integer \(a\) or you can switch the positions of the leading coefficient and the constant term (i.e. you can replace \(ax^2+bx+c\) by \(cx^2+bx+a\)). You start with the polynomial \(f=x^2+x+1\). Using the given operations, which of the following polynomials can you arrive at starting from \(f\)?

This problem is a part of Tessellate S.T.E.M.S.

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