Using a Known Factor

The factor theorem finds one factor. Division finds the rest. For ${x}^{3}+2{x}^{2}-5x-6$, the value at x = -1 is 0, so $x+1$ is a factor. Dividing by $x+1$ gives ${x}^{2}+x-6$. That factors as $\left(x+3\right)\left(x-2\right)$.

$${x}^{3}+2{x}^{2}-5x-6 = \left(x+1\right)\left(x+3\right)\left(x-2\right)$$

Which numbers should you try first? A whole-number root, an x that gives 0, divides the last number. Here that number is 6.