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Answer:
x9−1=(x−1)(x2+x+1)(x6+x3+1)
Explanation:
To factorize x9−1,
we can use the identity
a3−b3=(a−b)(a2+ab+b2).
Hence,
x9−1=(x3)3−13=(x3−1)(x6+x3+1)
factorizing x3−1 further
x9−1=(x3−1)(x6+x3+1)
= (x−1)(x2+x+1)(x6+x3+1)
Thus, it has 2 factors.
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