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Factorize: x^{3} + x - 3x^{2} - 3

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#### Solution

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

Taking x common in (x^{3} + x)

= x (x^{2} +1) - 3x^{2} - 3

Taking -3 common in (-3x^{2} - 3)

= x(x^{2} +1) - 3(x^{2} +1)

Now, we take (x^{2} +1) common

= (x^{2} +1)( x - 3)

`∴ x^3 + x - 3x^2 - 3 = (x^2 + 1)(x - 3)`

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