Question

# Factorise : $$\displaystyle n^{3}-3n-2$$ given that $$n+1$$ is a factor. The factors are

A
(n+1)2(n2)
B
(n+1)(n2)2
C
(n+1)2(n+2)
D
none of these

Solution

## The correct option is C $$\displaystyle \left ( n+1 \right )^{2}\left ( n-2 \right )$$the factors of $$n^{3}-3n-2$$ are$$= n^{3}-2n^{2}+2n^{2}-4n+n-2$$$$= n^{2}(n-2)+2n(n-2)+1(n-2)$$$$= (n-2)(n^{2}+2n+1)$$$$= (n-2)(n+1)^{2}$$Mathematics

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