CubicSolver.latex

p_0(1 - t)^3 + 3p_1t(1 - t)^2 + 3p_2t^2(1 - t) + p_3t^3
\\
p_0(1 - 3t + 3t^2 - t^3)
+ 3p_1(t - 2t^2 + t^3)
+ 3p_2(t^2 - t^3)
+ p_3t^3
\\
t^3(p_3 - 3p_2 + 3p_1 - p_0)
+ t^23(p_2 - 2p_1 + p_0)
+ t3(p_1 - p_0) + p_0
\\
18abcd - 4b^3d + b^2c^2 - 4ac^3 - 27a^2d^2
\\
(p_2 - 2p_1)^2(p_1)^2 - 4(1 - 3p_2 + 3p_1)p_1^3
\\
(p_2^2 - 4p_1p_2 + 4p_1^2)(p_1)^2
- 4p_1^3 + 12p_1^3p_2 + 12p_1^4
\\
p_1^2p_2^2 - 4p_1^3 + 8p_1^3p_2 + 16p_1^4
\\
p_1^2(p_2^2 + 8p_1p_2 - 4p_1 + (4p_1)^2)
\\
p_1^2((4p_1 + p_2)^2 - 4p_1)