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Factorisation by Common Factors

Factorise: ...

Question

Factorise: $3 x^{3} - x^{2} - 10 x$

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Solution

The given exprrssion $3 x^{3} - x^{2} - 10 x$ can be factorised as follows:

$3 x^{3} - x^{2} - 10 x = x (3 x^{2} - x - 10) = x (3 x^{2} - 6 x + 5 x - 10) = x [3 x (x - 2) + 5 (x - 2)] = x (3 x + 5) (x - 2)$

Hence, $3 x^{3} - x^{2} - 10 x = x (3 x + 5) (x - 2)$

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