x^3 + 9x^2 + 27x + 27 all divided by 2

Question

Help on how to solve that problem

Answer 1

(x³+9x²+27x+27)/2=½x³+9x²/2+27x/2+27/2, but is that all you want from this question?

The cubic factorises and one of its factors is x+3, because the polynomial is 0 when x=-3. To find the quadratic factor, we can use synthetic division:

-3 | 1  9   27    27

      1 -3 -18 | -27

      1  6    9 |    0 = x²+6x+9=(x+3)². So the polynomial is a perfect cube.

Therefore the answer can also be expressed ½(x+3)³.