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Question
Factorise: x4 - 5x2 - 36
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Solution
x4 - 5x2 - 36
= (x2)2 - 5x2 - 36
= (x2)2 - 9x2 + 4x2 - 36 ...{∵ -36 = -9 × 4 }
{-5 = -9 + 4}
= x2 (x2 - 9) + (x2 - 9)
= (x2 - 9)(x2 + 4)
= [x2 - (3)2] [x2 + 4]
= (x + 3)(x - 3)(x2 + 4)
= (x2 +4) (x + 3)(x - 3)
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