Question:
One of the factors of $\left(25 x^{2}-1\right)+(1+5 x)^{2}$ is
(a) $5+x$
(b) $5-x$
(c) $5 x-1$
(d) $10 x$
Solution:
(d) Now, (25x2 -1) + (1 + 5x)2
= 25x2 -1 + 1 + 25x2 + 10x [using identity, (a + b)2 = a2 + b2 + 2ab]
= 50x2 + 10x = 10x (5x+ 1)
Hence, one of the factor of given polynomial is 10x.
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