Question 14
One of the factors of $(25 x^{2} - 1) + (1 + 5 x)^{2}$ is

A) $5 + x$
B) $5 - x$
C) $5 x - 1$
D) $10 x$

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Solution

The answer is D.
$(25 x^{2} - 1) + (1 + 5 x)^{2}$
$= 25 x^{2} - 1 + 1 + 25 x^{2} + 10 x$ [Using identity, $(a + b)^{2} = a^{2} + b^{2} + 2 a b]$
$= 50 x^{2} + 10 x = 10 x (5 x + 1)$
Hence, one of the factor of given polynomial is 10x.

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Similar questions

One of the factors of $(25 x^{2} - 1) + (1 + 5 x)^{2}$ is

A) $5 + x$
B) $5 - x$
C) $5 x - 1$
D) $10 x$

One of the factors of $(25 x^{2} - 1) + (1 + 5 x)^{2}$ is

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

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