雙十字交乘

  \begin{align} 0x^4+{x^3} + 2\sqrt 3 {x^2} + 3x + \sqrt 3 -1 = 0 \\\begin{array}{*{20}{c}} 1 \\ 0 \\\end{array} \require{cancel}\xcancel{　　　　} \begin{array}{*{20}{c}} { + a} \\ { + 1} \end{array}\require{cancel}\xcancel{　　　　}\begin{array}{*{20}{c}} { + 1} \\ {\sqrt 3 - 1} && \end{array} \\ \left\{ \begin{gathered} a + 0 + \sqrt 3 - 1 = 2\sqrt 3 \\ a(\sqrt 3 - 1) + 1 = 3 \\ \end{gathered} \right. \Rightarrow a = \sqrt 3 + 1 \\ (x + \sqrt 3 - 1)({x^2} + (\sqrt 3 + 1)x + 1) = 0 \\ \end{align}