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Taking Out Common Factors

Factorise 5 x...

Question

Factorise $(5 x^{6} - 7 x^{3} - 6)$

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Solution

$(5 x^{6} - 7 x^{3} - 6)$
put $x^{3} = y$
$5 y^{2} - 7 y - 6 5 y^{2} - 10 y + 3 y - 6 = 5 y (y - 2) + 3 (y - 2) = (5 y + 3) (y - 2) = (5 x^{3}) (x^{3} - 2)$

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