Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$-x^{2}+2x+4=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
Now solve the equation $x=\frac{-2±2\sqrt{5}}{-2}$ when $±$ is plus. Add $-2$ to $2\sqrt{5}$.
$$x=\frac{2\sqrt{5}-2}{-2}$$
Divide $-2+2\sqrt{5}$ by $-2$.
$$x=1-\sqrt{5}$$
Now solve the equation $x=\frac{-2±2\sqrt{5}}{-2}$ when $±$ is minus. Subtract $2\sqrt{5}$ from $-2$.
$$x=\frac{-2\sqrt{5}-2}{-2}$$
Divide $-2-2\sqrt{5}$ by $-2$.
$$x=\sqrt{5}+1$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $1-\sqrt{5}$ for $x_{1}$ and $1+\sqrt{5}$ for $x_{2}$.
