Answer:
-8/3; 65/3
Step-by-step explanation:
If x-3 is a factor of a polynomial, it means that said polinomial evaluated at x=3 is 0. Let's apply it to both polynomials
[tex]3(3)^3-(a-b)(3)-8 =0\\(3)^3-(a+b)(3)+30 = 0[/tex]
At this point you have two condition linking a and b, we just have to write them in a slightly better looking way.
[tex]73 -3(a -b) =0\\57-3(a+b)=0[/tex]
by adding and subtracting the two equations you can find the two values
[tex]add:130-6b=0 \rightarrow b=\frac{65}3\\sub: 16+6a=0 \rightarrow a=-\frac83[/tex]
