According to the rational root theorum, which is a factor of the polynomial f(x) = 3x^3 -5x^2 - 12x + 20

We will find the rational zeros of f(x) = 3x^3 -5x^2 - 12x + 20

1) Arrange in descending order: f(x) = 3x^3 -5x^2 - 12x + 20

2) write down the factors of the constant term, 20. 
1,2, 4, 5, 10, 20 - these could all be the possible values of p.

3) write down the factors of the leading coefficient, 3.
1,3 - these are the possible values of q.
.
4) write down all the possible values of p/q. both positive and negative values must be written down. Simplify
1/1 ; 1/3 ; 2/1 ; 2/3 ; 4/1 ; 4/3 ; 5/1 ; 5/3 ; 10/1 ; 10/3 ; 20/1 ; 20/3
1 ; 0.33 ; 2 ; 0.67 ; 4 ;  1.33 ; 5 ; 1.67 ; 10 ; 3.33 ; 20 ; 6.67

5) use the simplified p/q in both positive and negative values in the synthetic division.  Pls. see attachment for my synthetic division.

Based on my computations, a factor of the polynomial f(x) = 3x^3 -5x^2 - 12x + 20 is:  x = -1.67 or x = -5/3

IF THESE ARE THE MISSING CHOICES:
A)2x + 1 B)2x - 1 C)3x+5 D)3x - 5.

MY ANSWER IS: D) 3x - 5.

In algebra, the rational root theorem states a constraint on rational solutions of a polynomial equation

with integer coefficients. Solutions of the equation are roots of the polynomial on the left side of the equation.

If and are nonzero, then each rational solution x, when written as a fraction in lowest terms satisfies

p is an integer factor of the constant term q is an integer factor of the leading coefficient

For the polynomial , Find factors of these coefficients:

factors of are factors of are

Therefore, possible roots are

Check all that apply:

Then

there are three possible factors

The last one can be rewritten as 3x-5, then