# 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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