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

facas9

facas9

Answered question

2021-05-25

Which of the following is the correct complete factorization of x41?

Answer & Explanation

crocolylec

crocolylec

Skilled2021-05-26Added 100 answers

Step 1
To find the complete factorization of x41.
Solution:
We know that,
a2b2=(a=b)(ab)
Factorizing the given expression using above identity.
x41=(x2)212
=(x2+1)(x21)
=(x2+1)(x212)
=(x2+1)(x+1)(x1)
Therefore, x41=(x2+1)(x+1)(x1).
Step 2
Hence, complete factorization of x41 is (x2+1)(x+1)(x1).

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