Which of the following is the factor of the polynomial $x^{3} - y^{3}$ ?

x + y

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x - y

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x^{2} + y^{2}

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None of these

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Solution

The correct option is B $x - y$
The given polynomial is of form $x^{n} - a^{n}$ , where n is odd.
So, by factor theorem, the factor will be $(x - a)$ .
Similarly, for the polynomial $x^{3} - y^{3}$ , the factor will be $(x - y)$ .
Thus, the correct answer is option (b).

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