Mathematics
Factorise the following:
x3 - 5x2 - x + 5
Factorisation
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Answer
x3 - 5x2 - x + 5 = x2(x - 5) - 1(x - 5)
= (x2 - 1)(x - 5).
Using identity,
a2 - b2 = (a - b)(a + b).
(x2 - 1)(x - 5) = (x - 1)(x + 1)(x - 5).
Hence, x3 - 5x2 - x + 5 = (x - 1)(x + 1)(x - 5).
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