H.C.F. of $x^{3} - 1$ and $x^{4} + x^{2} + 1$ is

x^{2} + x + 1

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x - 1

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x^{3} - 1

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x^{4} + x^{2} + 1

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Solution

The correct option is A $x^{2} + x + 1$
$x^{3} - 1 = (x - 1) (x^{2} + x + 1)$
$x^{4} + x^{2} + 1 = (x^{2} + x + 1) (x^{2} - x + 1)$
Clearly H.C.F of $x^{3} - 1$ and $x^{4} + x^{2} + 1$
i.e.H.C.F of $(x - 1) (x^{2} + x + 1)$ and $(x^{2} + x + 1) (x^{2} - x + 1)$ is $(x^{2} + x + 1)$
Option A is correct.

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Similar questions

x^{3} - 1

x^{4} + x^{2} + 1

If $x + \frac{1}{x} = 3$ , calculate $x^{2} + \frac{1}{x^{2}}, x^{3} + \frac{1}{x^{3}} a n d x^{4} + \frac{1}{x^{4}}$ .

x \neq 0

x + \frac{1}{x} = 2

x^{2} + \frac{1}{x^{2}} = x^{3} + \frac{1}{x^{3}} = x^{4} + \frac{1}{x^{4}}

x^{3} + x^{2} - x + 1

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