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प्रश्न
Factorise the following:
a4 – 3a2 + 2
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उत्तर
Let a2 = x
a4 – 3a2 + 2 = (a2)2 – 3a2 + 2
= x2 – 3x + 2
Product = 2 and sum = – 3
Split the middle term as – x and – 2x
x² – 3x + 2 = x2 – x – 2x + 2
= x(x – 1) – 2(x – 1)
= (x – 1)(x – 2)
a4 – 3a2 + 2 = (a2 – 1)(a2 – 2) ...[But a2 = x]
= (a + 1)(a – 1)(a2 – 2)
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