Question

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​

Answer 1

Answer:

ans is.43(x²-14)9²-4)7²4

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

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

EVALUATION

Here the given expression is

$\sf{ {x}^{17} - x }$

We now simplify it as below

$\sf{ {x}^{17} - x }$

$\sf{ = x({x}^{16} - 1) }$

$\sf{ = x({x}^{8} - 1)( {x}^{8} + 1) }$

$\sf{ = x({x}^{4} - 1)( {x}^{4} + 1)( {x}^{8} + 1) }$

$\sf{ = x({x}^{2} + 1)( {x}^{2} - 1 )( {x}^{4} + 1)( {x}^{8} + 1) }$

$\sf{ = x(x + 1)(x - 1)({x}^{2} + 1)( {x}^{4} + 1)( {x}^{8} + 1) }$

Hence $\sf{ ({x}^{6} + 1)}$ is not a factor

FINAL ANSWER

Hence the correct option is

$\sf{ 2) \: \: \: \: ({x}^{6} + 1)}$

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