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HCF and LCM

The HCF of th...

Question

The HCF of the polynomials $x^{3} - 3 x^{2} + x - 3 a n d x^{3} - x^{2} - 9 x + 9$ is

x - 3

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x - - 1

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x^{2} + 1

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(x - 1) (x - 3)

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Solution

The correct option is A $x - 3$
$x^{3} - 3 x^{2} + x - 3 = x^{2} (x - 3) + 1 (x - 3)$
$= (x - 3) (x^{2} + 1)$
$x^{3} - x^{2} - 9 x + 9 = x^{2} (x - 1) - 9 (x - 1)$
= $(x^{2} - 9) (x - 1) = (x + 3) (x - 3) (x - 1)$
$∴$ Reqd HCF $= (x - 3)$

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