If (y - 3) is a factor of $y^{3} - {2 y}^{2} - 9 y + 18$ then find the other two factors.

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Solution

$y^{3} - 2 y^{2} - 9 y + 18$
$= y^{2} (y - 2) - 9 (y - 2)$
$= (y - 2) (y^{2} - 9)$
$= (y - 2) (y - 3) (y + 3)$
$∴$ the other factors are $(y - 2)$ and $(y + 3)$

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