# How do you factor x^2 +1 - x?

${x}^{2} + 1 - x = {x}^{2} - x + 1$
is of the form $a {x}^{2} + b x + c$ with $a = 1$, $b = - 1$ and $c = 1$
The discriminant $\Delta$ is given by the formula:
$\Delta = {b}^{2} - 4 a c = {\left(- 1\right)}^{2} - \left(4 \times 1 \times 4\right) = 1 - 4 = - 3$
Since $\Delta < 0$ the equation ${x}^{2} - x + 1 = 0$ has no real roots and the quadratic ${x}^{2} - x + 1$ has no linear factors with real coefficients.