The factor of $5 x^{2} - 15 x - 7 x + 21$ is

(5 x - 1) (x - 7)

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(5 x - 7) (x - 3)

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(5 x + 3) (x - 7)

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(5 x + 7) (x - 3)

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Solution

The correct option is B $(5 x - 7) (x - 3)$
$5 x^{2} - 22 x + 21$
$= 5 x^{2} - 15 x - 7 x + 21$ (Rewrite $- 22 x$ as $- 15 x - 7 x$ to make grouping and factoring easier.)
$= 5 x^{2} - 15 x - 7 x + 21$
$= 5 x (x - 3) - 7 (x - 3)$
$= (5 x - 7) (x - 3)$
Therefore $5 x^{2} - 22 x + 21 = (5 x - 7) (x - 3)$

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