factorise:x⁴+4x³-x²-16x-12
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4x³ - 16x - (x⁴ - x² - 12)
= 4x(x²-4) - ((x²-4)(x²+3))
Notice (x²-4) is a common factor:
(x²-4) [4x - (x²+3)]
= (x²-4) [-x² + 4x - 3]
= -(x²-4) [x² - 4x + 3]
= -(x²-4) [(x - 3)(x -1)]
= -(x-2)(x+2)(x-3)(x-1)
= 4x(x²-4) - ((x²-4)(x²+3))
Notice (x²-4) is a common factor:
(x²-4) [4x - (x²+3)]
= (x²-4) [-x² + 4x - 3]
= -(x²-4) [x² - 4x + 3]
= -(x²-4) [(x - 3)(x -1)]
= -(x-2)(x+2)(x-3)(x-1)
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