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