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 $ax^{2}+bx+c=0$.
$$16x^{2}+8x-1=0$$
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 $x=\frac{-8±8\sqrt{2}}{32}$ when $±$ is plus. Add $-8$ to $8\sqrt{2}$.
$$x=\frac{8\sqrt{2}-8}{32}$$
Divide $-8+8\sqrt{2}$ by $32$.
$$x=\frac{\sqrt{2}-1}{4}$$
Now solve the equation $x=\frac{-8±8\sqrt{2}}{32}$ when $±$ is minus. Subtract $8\sqrt{2}$ from $-8$.
$$x=\frac{-8\sqrt{2}-8}{32}$$
Divide $-8-8\sqrt{2}$ by $32$.
$$x=\frac{-\sqrt{2}-1}{4}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-1+\sqrt{2}}{4}$ for $x_{1}$ and $\frac{-1-\sqrt{2}}{4}$ for $x_{2}$.
