Factors of a² − 1 − 2x − x²
The factors of \[ a^2-1-2x-x^2 \] 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
Solution
\[ a^2-1-2x-x^2 \]
\[ =a^2-(x^2+2x+1) \]
\[ =a^2-(x+1)^2 \]
\[ =(a+x+1)(a-x-1) \]
Therefore,
\[ \boxed{(c)\ (a+x+1)(a-x-1)} \]