$${\begin {array} {l} p(x) + q(x) = x^4 + x^2 + 3 \\ p(x) - q(x) = -x^4 + 5x^2 + 3 \\ p(x) \cdot q(x) = 3x^6 - 3x^4 - 6x^2 \end {array}}$$