Factors of $2 (a + b)^{2} - 9 (a + b) - 5$ are

a + b + 5

2 a + 2 b - 1

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a + b - 5

2 a + 2 b + 1

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a - b + 5

2 a - 2 b + 5

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None of these

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Solution

The correct option is D $a + b - 5$ , $2 a + 2 b + 1$
Given polynomial is $2 {(a + b)}^{2} - 9 (a + b) - 5$
Let $(a + b) = x$ .
Then, the polynomial becomes $2 x^{2} - 9 x - 5$
$= 2 x^{2} - 10 x + x - 5 = (x - 5) (2 x + 1)$
Replacing $x$ by $(a + b)$ it becomes $(a + b - 5) (2 a + 2 b + 1)$
$∴$ Required factors are $(a + b - 5)$ and $(2 a + 2 b + 1)$ .

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