Select the correct choice below.
(a) x^3 - 8 =?
(b) The polynomial is prime.
Select the correct choice below.
(a) x^3 - 8 =?
(b) The polynomial is prime.
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 )