(x-3) is a factor of 3x^3-7x^2-5x-3

The other factor is a polynomial (degree = 3-1 = 2)

Therefore 3x^3-7x^2-5x-3=(x-3)(ax^2+bx+c)

Expanding gives 3x^3-7x^2-5x-3 = ax^3 + (-3a+b)x^2 + (-3b+c)x - 3c

Identifying the same power terms

a=3

-3a+b=-7

-3b+c=-5

-3c=-3

Therefore

a=3

c=1

b=2