Which of the following is not a factor of x17 – x?
x2 – 1
x6 + 1
x4 – 1
x8 + 1
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manognapolikepad
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Which of the following is not a factor of x^17-x : (1) x^2-1 (2) x^6+1 (3) x^4-1 (4) x^8+1
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DanielSanthosh
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Answer:
Apply remainder theorem
x+1=0
x=−1
Put the value of x=−1 in all equations.
(i) x3+x2+x+1=(−1)3+(−1)2+(−1)+1=−1+1−1+1=0
Then x+1 is the factor of equation
(ii) x4+x3+x2+x+1=(−1)4+(−1)3+(−1)2+(−1)+1=1−1+1−1+1=1
This is not zero.Then x+1 is not the factor of equation
(iii) x4+3x3+3x2+x+1=(−1)4+3(−1)3+3(−1)2+(−1)+1=1
This is not zero.Then x+1 is not the factor of equation
(iv)x3−x2−(2+2)x+