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GCD of Polynomials

The HCF of ...

Question

The HCF of $(x^{2} - 9), (x^{3} - 27)$ and $(x^{2} - 8 x + 15)$ is:

x - 3

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x + 3

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(x - 3) (x^{2} + 3 x + 9)

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(x - 3) (x + 3) (x + 5) (x^{2} + 3 x + 9)

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Solution

The correct option is A $x - 3$
$(x^{2} - 9) = (x - 3) (x + 3)$
$(x^{3} - 27) = (x^{3} - 3^{3}) = (x - 3) (x^{2} - 3 x + 9)$
$(x^{2} - 8 x + 15) = (x - 3) (x - 5)$

$∴$ H.C.F. of $(x^{2} - 9), (x^{3} - 27)$ and $(x^{2} - 8 x + 15)$ is $x - 3$ .

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