Synthetic??

Since you do not know HOW you are supposed to solve this:

   As a follow on to cphill 's answer.....

IF   7x+8   is a factor....then   -8/7 is a root   you can do the synthetic division...or just substitute  -8/7 in to the equation to see if it will make it = zero

7 (-8/7)^3 - 55(-8/7)^2 - 135(-8/7) - 72       DOES = 0   

          so   7x + 8   IS a factor     (this is real easy if you have a calculator with a memory to store (-8/7) and then substitute it in.

You can do the same with the second one...... cphill already found   r-8 is NOT a factor.

For the first  one...if 7x + 8 is a factor then -8/7 must be a root

So.......

-8/7    [   7       - 55        -135       -72 ]

                        -8            72         72       

             ________________________

              7       -63          -63          0

We get a 0 remainder....so   7x + 8 is a factor

Second one  if r - 8 is a factor,  then  8 is a root

Remember that we need to account for the missing x term in the synthetic division

So we have

8 [  7    - 56   0     - 4  ]

              56   0       0

     _______________

       7       0    0     - 4

We do not get 0 as a remainder....so....r - 8 is not a factor