A good use of the remainder theorem

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 $R(x)$ .