Question

Which of the following is the correct complete factorization of x^{4} - 1?

Polynomial factorization
ANSWERED
asked 2021-05-25
Which of the following is the correct complete factorization of \(x^{4} - 1\)?

Answers (1)

2021-05-26
Step 1
To find the complete factorization of \(x^{4}−1\).
Solution:
We know that,
\(a^{2}-b^{2}=(a=b)(a-b)\)
Factorizing the given expression using above identity.
\(x^{4}-1=(x^{2})^{2}-1^{2}\)
\(=(x^{2}+1)(x^{2}-1)\)
\(=(x^{2}+1)(x^{2}-1^{2})\)
\(=(x^{2}+1)(x+1)(x-1)\)
Therefore, \(x^{4}-1=(x^{2}+1)(x+1)(x-1)\).
Step 2
Hence, complete factorization of \(x^{4}-1\ is\ (x^{2}+1)(x+1)(x-1)\).
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