# How do you factor 1/4+x+x^2?

$\frac{1}{4} + x + {x}^{2} = {\left(\frac{1}{2} + x\right)}^{2}$
Both $\frac{1}{4} = {\left(\frac{1}{2}\right)}^{2}$ and ${x}^{2}$ are perfect squares, so the only remaining question is whether the middle term matches when you square $\left(\frac{1}{2} + x\right)$:
${\left(\frac{1}{2} + x\right)}^{2} = {\left(\frac{1}{2}\right)}^{2} + 2 \left(\frac{1}{2}\right) x + {x}^{2} = \frac{1}{4} + x + {x}^{2}$