Question

How do you factor this expression: x^3 + 9x^2 + 27x + 27. Thanks! :)

Answer 1

Answer:

(x + 3)³

Step-by-step 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