Factor the following polynomials 11.) 3x3+3x2+x+1 and 12.) 6g3+8g2-15g-20

With 3 the leading coefficient and 1 the constant, either 1/3 or -1/3 is likely to be a root of the poly in #11.  Use synth. division to check this out:

           
(-1/3)  /  3   3   1      1
                  -1  -2/3  -1/9
           
             3    2   1/3    8/9   Since the remainder is not zero, -1/3 is                                                     unfortunately not a root and 3x+1 is not a factor.

A better approach may be factoring by grouping.  We see that 3x^3 + 3x^2 factors into 3x^2(x+1).  Also, x+1 factors into 1(x+1).  The common factor here is x+1.  So the given poly becomes (3x^2 + 1)(x+1)  (these are your 
factors).