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 $ax^{2}+bx+c=0$.
$$8x^{2}+x=0$$
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.
$$x=\frac{-1±\sqrt{1^{2}}}{2\times 8}$$
Take the square root of $1^{2}$.
$$x=\frac{-1±1}{2\times 8}$$
Multiply $2$ times $8$.
$$x=\frac{-1±1}{16}$$
Now solve the equation $x=\frac{-1±1}{16}$ when $±$ is plus. Add $-1$ to $1$.
$$x=\frac{0}{16}$$
Divide $0$ by $16$.
$$x=0$$
Now solve the equation $x=\frac{-1±1}{16}$ when $±$ is minus. Subtract $1$ from $-1$.
$$x=-\frac{2}{16}$$
Reduce the fraction $\frac{-2}{16}$ to lowest terms by extracting and canceling out $2$.
$$x=-\frac{1}{8}$$
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 $-\frac{1}{8}$ for $x_{2}$.
