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1 Pure Mathematics

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Question 209

The polynomial Q Q\,Q is defined by Q(x)=x3+3x2+2xQ(x)=x^3+3x^2+2xQ(x)=x3+3x2+2x.

a.

Use the factor theorem to show that (x+1)(x+1)(x+1) and (x+2)(x+2)(x+2) are factors of Q(x)Q(x)Q(x).

[2]
b.

Factorise Q(x)Q(x)Q(x) completely.

[2]
c.

Hence prove that Q(n)Q(n)Q(n) is divisible by 6 for every integer nnn.

[2]
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1 Pure Mathematics Questions

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