Answer:
(x + 3)³
Explanation:
Use rational root test to check for possible rational roots.
Factors of 27 are 1, 3, 9, and 27.
Factors of 1 are 1.
Possible rational roots are:
±1/1, ±3/1, ±9/1, ±27/1
Checking each one, we find that -3 is a root. So x + 3 is a factor.
Knowing that, we can use grouping to factor.
x³ + 9x² + 27x + 27
x³ + 9x² + 18x + 9x + 27
x (x² + 9x + 18) + 9 (x + 3)
x (x + 6) (x + 3) + 9 (x + 3)
(x + 3) (x (x + 6) + 9)
(x + 3) (x² + 6x + 9)
(x + 3) (x + 3)²
(x + 3)³