$Divide (x^{2} - 2 x - 35) by (x - 7)$

(x - 5)

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(x + 3)

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(x - 3)

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(x + 5)

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Solution

The correct option is D $(x + 5)$
$Given: \frac{x^{2} - 2 x - 35}{(x - 7)} . . . (i)$

Comparing $x^{2} - 2 x - 35$ with the identity $x^{2} + (a + b) x + a b$
$We note that, (a + b) = - 2 and a b = - 35$

$S o, (- 7) + 5 = - 2 and (- 7) (5) = - 35$

Hence,
$x^{2} - 2 x - 35$
$= x^{2} - 7 x + 5 x - 35$
$= x (x - 7) + 5 (x - 7)$
$= (x + 5) (x - 7)$

From (i), we get
$\frac{x^{2} - 2 x - 35}{(x - 7)} = \frac{(x + 5) (x - 7)}{(x - 7)} = (x + 5)$

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