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 $ax^{2}+bx+c=0$.
$$x^{2}-8x+4=0$$
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 $x=\frac{8±4\sqrt{3}}{2}$ when $±$ is plus. Add $8$ to $4\sqrt{3}$.
$$x=\frac{4\sqrt{3}+8}{2}$$
Divide $8+4\sqrt{3}$ by $2$.
$$x=2\sqrt{3}+4$$
Now solve the equation $x=\frac{8±4\sqrt{3}}{2}$ when $±$ is minus. Subtract $4\sqrt{3}$ from $8$.
$$x=\frac{8-4\sqrt{3}}{2}$$
Divide $8-4\sqrt{3}$ by $2$.
$$x=4-2\sqrt{3}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $4+2\sqrt{3}$ for $x_{1}$ and $4-2\sqrt{3}$ for $x_{2}$.
