Factories $x^{3} - 9 x^{2} + 26 x - 24$

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Solution

Let $f (x) = x^{3} - 9 x^{2} + 26 x - 24$
$\Rightarrow f (x) = x^{3} - 4 x^{2} - 5 x^{2} + 20 x + 6 x - 24$
$= x^{2} (x - 4) - 5 x (x - 4) + 6 (x - 4)$
$= (x - 4) (x^{2} - 5 x + 6)$
$= (x - 4) (x^{2} - 2 x - 3 x + 6)$
$= (x - 4) (x (x - 2) - 3 (x - 2))$
$= (x - 4) (x - 2) (x - 3)$
$∴$ the factors are $(x - 2) (x - 3) (x - 4)$

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