Divide $(9 x^{2} - 24 x + 16)$ by $(3 x - 4)$

3 x - 4

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4 x - 3

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(3 x - 4) (3 x - 4)

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9 x^{2} - 16

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Solution

The correct option is A $3 x - 4$
$(9 x^{2} - 24 x + 16) \div (3 x - 4)$ = $\frac{(9 x^{2} - 24 x + 16)}{(3 x - 4)}$

We have to find factors of $144$ such that their sum is $- 24$ .
The factors are $- 12$ and $- 12$ .

$∴ 9 x^{2} - 24 x + 16 = 9 x^{2} - 12 x - 12 x + 16$
$= 3 x (3 x - 4) - 4 (3 x - 4)$
$= (3 x - 4) (3 x - 4)$

$∴ \frac{(9 x^{2} - 24 x + 16)}{(3 x - 4)}$ = $\frac{(3 x - 4)^{2}}{3 x - 4}$

$= 3 x - 4$

So, option A is correct.

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