TeX Quellcode:

\begin{array}{lrclcll} & \mathbb{D} &=& \mathbb{R} \cr\cr& (2x^3+8x^2-6x)(9x^3-30)(4x^4-12x^2+2) &=& 0 \cr\cr\text{Faktor 1:} & 2x^3+8x^2-6x &=& 0 \cr & x(2x^2+8x-6) &=& 0 &\vert& \text{Satz vom Nullprodukt} \cr\cr\text{Faktor 1.1:} & x_1 &=& 0 \cr\cr \text{Faktor 1.2:} & 2x^2+8x-6 &=& 0 &\vert& :2 \cr & x^2+4x-3 &=& 0 &\vert& \text{p-q-Formel} \cr& x_{2,3} &=& -2\pm\sqrt{2^2+3} \cr\cr & x_{2} &=& -2+\sqrt{7} \approx 0{,}65 \cr& x_{3} &=& -2-\sqrt{7} \approx -4{,}65 \cr\cr\text{Faktor 2:} & 9x^3-30 &=& 0 &\vert& +30 \cr & 9x^3 &=& 30 &\vert& :9 \cr & x^3 &=& \dfrac{10}{3} &\vert& \sqrt[3]{} \cr& x_4 &=& \sqrt[3]{\dfrac{10}{3}} \approx 1{,}49 \cr\cr\text{Faktor 3:} & 4x^4-12x^2+2 &=& 0 &\vert& :4 \cr & x^4-3x^2+\dfrac12 &=& 0\end{array}