F(x)= 9x^3 + 10x^2 - 17x - 2 one zero given is -2

Repeat the process until you finish the long division. Be careful to subtract the ENTIRE polynomial you place beneath the former. It's easy to subtract when all terms are positive, but sometimes they are negative, in which case subtracting a negative --> adding. It helps if you write parentheses around the polynomial to be subtracted.
For your problem, my long division came out with 9x^2-8x-1.
That means 9x^3 + 10x^2 - 17x - 2 = (9x^2-8x-1)(x+2). Yay! Second degree is easier. Factor as you normally would.
9x^3 + 10x^2 - 17x - 2 = (9x^2-8x-1)(x+2) = (9x+1)(x-1)(x+2)
Now recall that we want to find the x-coordinate where each of these roots = 0, so
9x+1 = 0 and x-1 = 0, leading to x= -1/9 and x=1.
Plug these values back into your original equation to make sure they are correct (and you didn't make any little mistakes on the path getting here).
9(1)^3 + 10(1)^2 - 17(1) - 2 =9 + 10 -17 -2 = 0 :)
9(-1/9)^3 + 10(-1/9)^2 - 17(-1/9) - 2 = -1/81 + 10/81 +153/81 - 162/81 = 0
Hooray! Don't you love it when checking your answer is WAY faster than looking through your work?
Hope that helps and good luck!