Mathematics
x4 + x2 + 1
Factorisation
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Answer
Given,
x4 + x2 + 1
Adding and subtracting x2 in the polynomial,
⇒ x4 + x2 + 1 + x2 - x2
= x4 + 2x2 + 1 - x2
= (x2)2 + 2 × x2 × 1 + (1)2 - (x)2
= (x2 + 1)2 - (x)2
= (x2 + 1 + x)(x2 + 1 - x).
Hence, x4 + x2 + 1 = (x2 + 1 + x)(x2 + 1 - x).
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