Question

According to the rational root theorem, which is a factor of the polynomial

Answer 1

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.