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