Mathematics
Factorise the following:
x3 + x + 2
Factorisation
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Answer
x3 + x + 2 = x3 + x + 1 + 1.
= x3 + 1 + x + 1
= x3 + 13 + x + 1
We know that,
a3 + b3 = (a + b)(a2 - ab + b2).
x3 + 13 + x + 1 = (x + 1)(x2 - x + 1) + (x + 1)
= (x + 1)(x2 - x + 1 + 1)
= (x + 1)(x2 - x + 2).
Hence, x3 + x + 2 = (x + 1)(x2 - x + 2).
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