Rational Roots Theorem indicates possible roots to check are -27, -9, -3, -1, 1, 3, 9, 27.
Try using synthetic division to check for any or all of them. Remainder 0 means, the checked value is a root of the given polynomial.
x-3 factor is the root or zero, 3.
3 | 1 -4 -6 36 -27
| 3 -3 -27 27
|____________________________
1 -1 -9 9 0
Test again using the resulting coefficients from that result.
3 | 1 -1 -9 9
|
| 3 6 -9
|____________________________
1 2 -3 0
Resulting coefficients now mean
which factorizes as
The full factorization of the given polynomial is .