Factor x^3 - 8

Question

Select the correct choice below.

(a) x^3 - 8 =?

(b) The polynomial is prime.

Answer 1

Another factor or prime? Another cubic. Let's review our top three method for attacking this.

grouping • sum or difference of cubes • simplify and factor quadratic

This is when it's good to know your basic cubics just as well as you know your perfect squares!

2^3 = 8 so we can rewrite this as the difference of cubes.

x^3 - 8 = x^3 - 2^3

The difference of cubes is one of those simplifications you want to memorize.

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

For x^3 - 2^3, substitute 'x' for 'a' and '2' for 'b'.

Now you'll have a quadratic to factor or declare prime. 

Again, remember that if you can factor the quadratic, you'll have three factors total in your answer:

(x-2)(x     )(x     )