The LCM and HCF of two polynomials are respectively ${(2 a - 5)}^{2} (a + 1) a n d (2 a - 5)$ If one of the polynomials is $4 a^{2} - 20 a + 25$ the other one is

4 a^{2} + 20 a + 5

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4 a^{2} - 25

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2 a^{2} + 3 a - 5

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2 a^{2} - 3 a - 5

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Solution

The correct option is D $2 a^{2} - 3 a - 5$
LCM= $(2 a - 5) (2 a - 5) (a + 1)$
HCF= $(2 a - 5)$
One polynomial= $4 a^{2} - 20 a + 25$
$\Rightarrow 4 a^{2} - 10 a - 10 a + 25$
$\Rightarrow 2 a (2 a - 5) - 5 (2 a - 5)$
$\Rightarrow (2 a - 5) (2 a - 5)$
$L C M \times H C F = P r o d u c t o f t w o n u m b e r$
Let another number is x
$(2 a - 5) (2 a - 5) (a + 1) (2 a - 5) = (2 a - 5) (2 a - 5) \times x$
$x = \frac{(2 a - 5) (2 a - 5) (a + 1) (2 a - 5)}{(2 a - 5) (2 a - 5)}$
$x = (a + 1) (2 a - 5) \Rightarrow 2 a^{2} - 3 a - 5$

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