Factor the polynomial. x^{16}-1

Ernest Ryland

Ernest Ryland

Answered question

2021-12-14

Factor the polynomial. x161

Answer & Explanation

Maria Lopez

Maria Lopez

Beginner2021-12-15Added 32 answers

Step 1
To factor the polynomial: x161
Solution:
We have identity a2b2=(a+b)(ab)
Using the above identity, we will factor the given expression.
x161=(x8)212
=(x8+1)(x81)
=(x8+1)((x4)212)
=(x8+1)(x4+1)(x41)
=(x8+1)(x4+1)((x2)212)
=(x8+1)(x4+1)(x2+1)(x21)
=(x8+1)(x4+1)(x2+1)(x+1)(x1)
Step 2
Hence, required answer is x161=(x8+1)(x4+1)(x2+1)(x+1)(x1).

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