Find The H C F ? If

The H C F of X8 – 1 and X4 + 2 X3 – 2 X – 1 is :

  1. X2 + 1
  2. X – 1
  3. X2 – 1
  4. X + 1
Desire Adnan Default Asked on 18th August 2015 in Maths.
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1 Answer(s)

Answer: (3) X2 – 1

Explanation:-

X2 + 1
The factors of X8 – 1 = (X2)3 – (1)3
= (X2 – 1) (X4 + 1 + 2 X2)

The factors of X4 + 2 X3 – 2 X – 1 = X4 – 1 + 2 X3 – 2 X
= (X2 – 1) (X2 + 1 ) + 2 X (X2 – 1)
= (X2 – 1) (X2 + 1 + 2 X)
H C F = (X2 – 1)

Then, the H C F of X8 – 1 and X4 + 2 X3 – 2 X – 1 is X2 – 1.

Hence, the answer is X2 – 1.

 

Anurag Mishra Professor Answered on 21st August 2015.
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