x^4+(p+1)x^2+p^2+2p+1/4=(x^2)^2+2\cdot\frac{p+1}{2}x^2+(\frac{p+1}{2})^2-(\frac{p+1}{2})^2+p^2+2p+1/4=(x^2+\frac{p+1}{2})^2+\frac{-p^2-2p-1}{4}+p^2+2p+1/4=(t+\frac{p+1}{2})^2+3p^2+6p