Answer
$9x^{3}+18x^{2}-x-2=(x+2)(3x-1)(3x+1)$
Work Step by Step
$9x^{3}+18x^{2}-x-2$
Group the first and third terms together. Do the same with the second and fourth terms:
$9x^{3}+18x^{2}-x-2=(9x^{3}-x)+(18x^{2}-2)=...$
Take out common factor $x$ from the first parentheses and common factor $2$ from the second parentheses:
$...=x(9x^{2}-1)+2(9x^{2}-1)=...$
Take out common factor $(9x^{2}-1)$:
$...=(x+2)(9x^{2}-1)=...$
Finally, factor the difference of squares in the second parentheses:
$...=(x+2)(3x-1)(3x+1)$
