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Question

The expression x9x has:

A
5 factors
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B
4 factors
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C
2 factors
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D
3 factors
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Solution

The correct option is A 5 factors
x9x=x(x81)

=x[(x4)21]

=x[(x4)212]=x(x41)(x4+1)

(Using a2b2=(ab)(a+b))

=x[(x2)212](x4+1)

=x(x21)(x2+1)(x4+1)

=x(x1)(x+1)(x2+1)(x4+1)

Hence, the expression x9x has 5 factors, namely,
x,(x1),(x+1),(x2+1) and (x4+1)

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