Which of the following is a factor of x³ - 729?
x - 9
x + 9
x² + 18x + 81
None of the above

Solution:

The equation x³ - 729 can be rewritten as:

x³ - (9)³

We know that a³ - b³ = (a - b)(a² + ab + b²)

Therefore,

x³ - (9)³ = (x - 9)(x² + (x)(9) + 9²)

= (x - 9)(x² + 9x + 81)

Therefore (x - 9) and (x² + 9x + 81) are the factors of x³ - 729

Which of the following is a factor of x³ - 729?

Summary:

(x - 9) is a factor of x³ - 729.