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## 'Polynomial Relations' printed from http://nrich.maths.org/

Given any two polynomials in a single variable it is always
possible to eliminate the variable and obtain a formula showing the
relationship between the two polynomials.

Let $p(x) = x^2 + 2x$ and $q(x) = x^2 + x + 1$ then, using a method
which does not depend on knowing the answer, show that the
relationship between the polynomials is:

\[ p^2 - 2pq + q^2 + 3p - 4q + 3 = 0 \]