According to the rational root theorem, which is a factor of the polynomial f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35 a) 2x - 7 b) 2x + 7 c) 3x - 7 d) 3x + 7

Supposing 2x-7 were a factor, then 7/2 would be a root.  Use synth. div. to determine whether 7/2 actually is a root:

         
7/2   /   6    -21     -4    24    -35
                   21      0    -14    35
       
            6      0      -4     10     0

Since the remainder is zero, 7/2 is a root and 2x - 7 is a factor.

You could check out the other possible factors in the same manner.