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 $ax^{2}+bx+c=0$.
$$4x^{2}+35x+2=0$$
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 $x=\frac{-35±\sqrt{1193}}{8}$ when $±$ is plus. Add $-35$ to $\sqrt{1193}$.
$$x=\frac{\sqrt{1193}-35}{8}$$
Now solve the equation $x=\frac{-35±\sqrt{1193}}{8}$ when $±$ is minus. Subtract $\sqrt{1193}$ from $-35$.
$$x=\frac{-\sqrt{1193}-35}{8}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-35+\sqrt{1193}}{8}$ for $x_{1}$ and $\frac{-35-\sqrt{1193}}{8}$ for $x_{2}$.
