Factorize 84-2r-2r2.

Factorize $84-2r-{2r}^{2}.$

1. A
$-2\left(r+6\right)\left(r+7\right)$
2. B
$-2\left(r-6\right)\left(r+7\right)$
3. C
$-2\left(r-6\right)\left(r-7\right)$
4. D
$-2\left(r+6\right)\left(r-7\right)$

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Solution:

Given, $84-2r-{2r}^{2}.$
Rewrite the expression by arranging the degree in descending order and taking -2 as common, we get,
$84-2r-{2r}^{2}$
$-2\left({r}^{2}+r-42\right)$
Factorize the equation by splitting the middle term whose sum is 1 and product is -42.
$⇒-2\left({r}^{2}+7r-6r-42\right)$
$⇒-2\left(r\left(r+7\right)-6\left(r+7\right)\right)$ $⇒-2\left(r-6\right)\left(r+7\right)$
The factor is $-2\left(r-6\right)\left(r+7\right)$.
Therefore, option 2 is correct.

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