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The factors of $25 x 2 − 1 + (1 + 5 x) 2$ are [[1]] and [[2]].

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answer is 10 X AND 5 X + 1.

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Detailed Solution

The factors of

25 x 2 − 1 + (1 + 5 x) 2

are

10 x

and

5 x + 1 .

The given polynomial is,

25 x 2 − 1 + (1 + 5 x) 2

We use the concept of algebraic identities to solve the given polynomial.
By expanding the bracket, we get,

⇒ 25 x 2 − 1 + 1 + 5 x 2

⇒ = 5 x 2 − 1 + 1 + 5 x 2

Apply the algebraic identity,

a + b a − b = a 2 − b 2

Therefore,

⇒ 5 x + 1 5 x − 1 + 1 + 5 x 2

⇒ 5 x + 1 5 x − 1 + 1 + 5 x

⇒ 10 x 5 x + 1

Thus, the factors of the polynomial are

10 x 5 x + 1 .

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