Identify all the factors of this polynomial when it is factored completely

27x^2-153x-90

1. 3
2. 9
3. x-5
4. x+5
5. 3x-2
6. 3x+2
7. 3x-15
8. 9x+6

The given function is
f(x) = 27x² - 153x - 90

Factor out 9.
f(x) = 9(3x² - 17x - 10)

Note that 
10 = 2*5
(3x)*5 = 15x
x*2 = 2x
-(3x)*5 - x*2 = -15x - 2x = -17x

Therefore
3x² - 17x - 10 = (3x - 2)(x - 5)

The function factors completely into
f(x) = 9(3x - 2)(x - 5)

Test the given answers.
1. 3 is a factor of 9        TRUE
2. 9 is a factor               TRUE
3. x - 5 is a factor          TRUE
4. x + 5 is not a factor   FALSE
5. 3x - 2 is a factor        TRUE
6. 3x + 2 is not a factor  FALSE
7. 3x - 15 = 3(x - 5) is a factor because of 3 and (x-5)  TRUE
8. 9x+6 = 3(3x+2) is not a factor because (3x+2) is not a factor  FALSE

1, 2, 3, 5 and 7  are factors.