Phân tích thành nhân tử

To factorize the expression x^3 + 9x^2 + 27x + 27, we can use the factor theorem.

First, we check if x = -1 is a factor of the expression by substituting x = -1 into the expression:

(-1)^3 + 9(-1)^2 + 27(-1) + 27 = -1 + 9 + (-27) + 27 = 0

Since the expression evaluates to 0 when x = -1, we know that (x + 1) is a factor.

Using synthetic division, we can divide the expression by (x + 1):

-1 | 1 9 27 27
| -1 -8 -19 -8
|________________
1 8 8 19

The quotient is x^2 + 8x + 8, and the remainder is 19.

Therefore, x^3 + 9x^2 + 27x + 27 = (x + 1)(x^2 + 8x + 8) + 19.