Factorise $9 z^{3} - 27 z^{2} - 100 z + 300$ if it is given that $3 z + 10$ is a factor of it?

f (z) = (z - 10) (3 z + 10)

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f (z) = (z - 3) (3 z + 10) (3 z - 10)

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f (z) = (3 z + 10) (3 z - 10)

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f (z) = (3 z + 10) (3 z - 12)

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Solution

The correct option is B $f (z) = (z - 3) (3 z + 10) (3 z - 10)$
Let $f (z) = 9 z^{3} - 27 z^{2} - 100 z + 300$
$3 z + 10$ is a factor of $f (z)$ .

$f (z) = 9 z^{3} - 27 z^{2} - 100 z + 300$
$= (3 z + 10) [3 z^{2} - 19 z + 30]$
$= (3 z + 10) [3 z^{2} - 10 z - 9 z + 30]$
$= (3 z + 10) [(3 z - 10) - 3 (3 z - 10)]$
$f (z) = (3 z + 10) (3 z - 10) (z - 3)$

So, the correct answer is option (b).

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