Factorise $3 x^{4} - 10 x^{3} + 5 x^{2} + 10 x - 8$

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Solution

Factorisation:
$3 x^{4} - 10 x^{3} + 5 x^{2} + 10 x - 8$
$= 3 x^{4} - 3 x^{3} - 7 x^{3} + 7 x^{2} - 2 x^{2} + 2 x + 8 x - 8$
$= 3 x^{3} (x - 1) - 7 x^{2} (x - 1) - 2 x (x - 1) + 8 (x - 1)$
$= (x - 1) (3 x^{3} - 7 x^{2} - 2 x + 8)$
$= (x - 1) (3 x^{3} + 3 x^{2} - 10 x^{2} - 10 x + 8 x + 8)$
$= (x - 1) {3 x^{2} (x + 1) - 10 x (x + 1) + 8 (x + 1)}$
$= (x - 1) (x + 1) (3 x^{2} - 10 x + 8)$
$= (x - 1) (x + 1) (3 x^{2} - 6 x - 4 x + 8)$
$= (x - 1) (x + 1) {3 x (x - 2) - 4 (x - 2)}$
$= (x - 1) (x + 1) (x - 2) (3 x - 4)$

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