factor $\sum_i^4 p_i x^i$

Question

The polynomial $f(x)= \sum_{i=0}^4 p_i x^i $ whose real coefficients are: $$ p_4 = (L^2 + s^2) ^2 \\ p_3= -4 L^2 (L^2 + s^2)\\ p_2 = 6 L^4 + 2 L^2s^2 \\ p_1 = -4 L^4 \\ p_0= L^4 - V^2\\ $$ can be factored as $ \left[ \left(L^2 + s^2 \right)x^2-2L^2x+L^2+V \right] \left[ \left(L^2 + s^2 \right)x^2-2L^2x+L^2-V \right]$. However, it's difficult to factor the polynomial with the following coefficients: $$ p_4 = (L^2 + s^2) ^2 \\ p_3= -4 L^2 (L^2 + s^2)\\ p_2 = 6 L^4 + 2 L^2s^2+L^2-s^2 \\ p_1 = -4 L^4 -2L^2 \\ p_0= L^4 +L^2+ \frac{1}{4}- V^2\\ $$ I find the negative $-s^2$ term in $p_2$ is tricky (Factorization becomes very easy when $p_2 = 6 L^4 + 2 L^2s^2+L^2+s^2$ instead). Any suggestions?