Question

The factors of a² - 1 - 2x - x²  are

A. (a - x + 1)(a - x - 1) 

B. (a + x - 1)(a - x + 1) 

C. (a + x + 1)(a - x - 1) 

D. none of these

Answer 1

We have,

\(=a^{2}-1-2\text{x}-\text{x}^{2}\)

\(=a^{2}-(1+2\text{x}+\text{x}^{2})\)

\(=a^{2}-(1+\text{x})^{2}\)

\(=(a-1-\text{x})(a+1+\text{x})\)

\([a^{2}-b^{2}=(a+b)(a-b)]\)

Thus, the factors of

\(a^{2}-1-2\text{x}-\text{x}^{2}\,are \,(a-1-\text{x})(a+1+\text{x}).\)