# How do you factor x^2+x+2?

May 8, 2015

${x}^{2} + x + 2$ is not factorable using rational numbers. This means that no rational numbers added together equal $1$ ($x$ in equation) and multiplied together equal $2$.

You can find the imaginary answer to ${x}^{2} + x + 2 = 0$ (an equation, notice the $=$), however.

Using the quadratic formula: $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$x$ would then equal $\frac{- 1 \pm i \sqrt{7}}{2}$

and the factors would be
${x}^{2} + x + 2 = \left(x + \frac{1 + \sqrt{7} i}{2}\right) \left(x + \frac{1 - \sqrt{7} i}{2}\right)$