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Mathematics

Factorise :

4x4 - x2 - 12x - 36

Factorisation

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Answer

Given,

    4x4 - x2 - 12x - 36

= 4x4 - [x2 + 12x + 36]

= 4x4 - [x2 + 6x + 6x + 36]

= 4x4 - [x(x + 6) + 6(x + 6)]

= 4x4 - (x + 6)(x + 6)

= (2x2)2 - (x + 6)2

= (2x2 + x + 6)(2x2 - x - 6).

= (2x2 + x + 6)(2x2 - 4x + 3x - 6)

= (2x2 + x + 6)[2x(x - 2) + 3(x - 2)]

= (2x2 + x + 6)(x - 2)(2x + 3).

Hence, 4x4 - x2 - 12x - 36 = (2x2 + x + 6)(x - 2)(2x + 3).

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