How do you factor x² - x - 90?

$\left(x - 10\right) \left(x + 9\right)$
To factor an expression in the form $a {x}^{2} + b x + c$, find two numbers that multiply to get c and add to get b. For the expression $\left({x}^{2} - x - 90\right)$, the factors of -90 are $\pm 1 , \pm 2 , \pm 3 , \pm 5 , \pm 6 , \pm 9 , \pm 10 , \pm 15 , \pm 18 , \pm 30 , \pm 45 , \mathmr{and} \pm 90$ (Note: $\pm 2$ means "plus or minus 2" or 2 and -2).
Thus, the factors of $\left({x}^{2} - x - 90\right)$ are $\left(x - 10\right)$ and $\left(x + 9\right)$ or $\left(x - 10\right) \left(x + 9\right)$