Choose one of the factors of x³ - 1331. 
x - 11, x² - 11x + 121, x² + 22x + 121, None of the above

Solution:

We will be use the algebraic identity a³ - b³ = (a - b)(a² + ab + b²)

Since we know that 1331 is a cube root of 11.

Using the identity a³ - b³ = (a - b)(a² + ab + b²)

x³ - 1331 = x³ - (11)³

= (x - 11)(x² + 11 × x + (11)²)

= (x - 11)(x² + 11x + 121)

As we can see that (x - 11) and (x² + 11x + 121) are the factors of x³ - 1331.

Choose one of the factors of x³ - 1331.

Summary:

The factors of x³ - 1331 are (x - 11) and (x² + 11x + 121).