Help with factoring this one:
x^9+1
(x^3+1) (x^3-x^3+1)
Is this correct?
you can factor the x^3 + 1 again into
(x+1)(x^2 - x + 1), your other factor was wrong, should have been x^6 - x^3 + 1
so
x^9 + 1 = (x+1)(x^2 - x + 1)(x^6 - x^3 + 1)
THANKS!
Yes, your answer is correct. The factoring of the expression x^9 + 1 as (x^3 + 1)(x^6 - x^3 + 1) is accurate.
To verify this factorization, you can use the product of powers rule and the difference of cubes formula.
First, consider (x^3 + 1) as factor 1.
Using the sum of cubes formula, we can factor x^3 + 1 as (x + 1)(x^2 - x + 1).
Now, focus on the remaining expression (x^6 - x^3 + 1) as factor 2.
This expression cannot be directly factored as a difference of cubes or any other known pattern, but we can still check if this factor can be multiplied by (x^3 + 1) to get the original polynomial x^9 + 1.
To determine this, we can multiply (x^3 + 1) and (x^6 - x^3 + 1) and verify if it simplifies back to x^9 + 1:
(x^3 + 1)(x^6 - x^3 + 1) = x^9 + x^6 - x^6 - x^3 + x^3 + 1 = x^9 + 1.
Since the result is equal to the original expression, the factorization is correct.
Therefore, the factored form of x^9 + 1 is (x^3 + 1)(x^6 - x^3 + 1).