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Q.

Which one of the following is a factor of $(25 x^{2} - 1) + {(1 + 5 x)}^{2}$ ?

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a

25 x + 1

b

5 x

c

(x + 1)

d

10 x

answer is D.

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Detailed Solution

Given expression is

(25 x^{2} - 1) + {(1 + 5 x)}^{2}

.
We know that,

a + b 2 = a 2 + b 2 + 2 a b .

25 x 2 − 1 + 1 + 5 x 2 = 25 x 2 − 1 + 1 + 25 x 2 + 10 x = 50 x 2 + 10 x = 10 x 5 x + 1

Hence, one of the factors of given polynomial is 10x.
The correct option is (4).

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