Mathematics
Factorise the following:
x4 + 3x2 + 4
Factorisation
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Answer
x4 + 3x2 + 4
Above terms can be written as,
(x2)2 + 3(x2) + 4 = (x2)2 + 4x2 - x2 + 22
= (x2 + 22)2 - (x2)
We know that,
(a2 - b2) = (a + b)(a - b)
∴ (x2 + 22)2 - (x2) = (x2 + 2 + x)(x2 + 2 - x)
= (x2 + x + 2)(x2 - x + 2)
Hence, x4 + 3x2 + 4 = (x2 + x + 2)(x2 - x + 2).
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