# A good use of the remainder theorem

Algebra Level 4

A polynomial $$P(x)$$ divided by $$x ^{2}+x+1$$ give us a remainder of $$-x+1$$ and when divided by $$x ^ {2} - x +1$$ has a remainder of $$3x+5$$. Knowing that the remainder of the division of $$P(x)$$ for $$x ^ {4} + x ^{2} + 1$$ is $$R(x)$$ a polynomial of the third degree, evaluate the sum of the squares of the coefficients of $$R(x)$$.

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