What are all real solutions to x³ + 2x² - 9x - 18 = 0?

Factor by grouping: $x^3+2x^2-9x-18=x^2(x+2)-9(x+2)=(x+2)(x^2-9)=(x+2)(x-3)(x+3)$. Setting each factor to zero gives $x=-2$, $x=3$, and $x=-3$, choice F. Check $x=-2$: $-8+8+18-18=0$. Choice G reverses the sign of the first root, giving $2$, but $x=2$ gives $8+8-18-18=-20$, not zero. Choice H ($-2,9$) and choice J ($2,9,-9$) use $9$ and $-9$ as roots, but those numbers are values of $x^2$ rather than of $x$; the actual roots of this cubic are all small. Always substitute a candidate back into the original equation.