Factorise:

$4 x^{4} - x^{2} - 12 x - 36$

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Solution

$4 x^{4} - x^{2} - 12 x - 36 \Rightarrow 4 x^{4} - (x^{2} + 12 x + 36) \Rightarrow 4 x^{4} - (x + 6)^{2} \Rightarrow (2 x^{2})^{2} - (x + 6)^{2} \Rightarrow (2 x^{2} + (x + 6)) (2 x^{2} - (x + 6)) \Rightarrow (2 x^{2} + x + 6) (2 x^{2} - x - 6) \Rightarrow (2 x^{2} + x + 6) (2 x^{2} - 4 x + 3 x - 6) \Rightarrow (2 x^{2} + x + 6) (2 x (x - 2) + 3 (x - 2)) \Rightarrow (2 x^{2} + x + 6) (2 x + 3) (x - 2)$

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