$Find the Highest Common Factor of the polynomials x^{2} - 6 x + 9 and x^{2} - 9.$

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Solution

$Factorizing x^{2} - 6 x + 9 by using the identities (a - b)^{2}, we get$
$(x)^{2} - 2 (x) (3) + (3)^{2}$
$= (x - 3)^{2}$
$= (x - 3) (x - 3)$
$Also, factorizing x^{2} - 9, we get$
$(x)^{2} - (3)^{2}, by using the identities of a^{2} - b^{2} .$
$= (x + 3) (x - 3)$
$Therefore, H.C.F. of x^{2} - 6 x + 9 and x^{2} - 9 is (x - 3) .$

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