Question

Mark the correct alternative in each of the following: The factors of a² − 1 − 2x − x² are

Options

• (a − x + 1) (a − x − 1)

• (a + x − 1) (a − x + 1)

• ` (a+x+1)(a- x -1)`

• none of these

Answer 1

The given expression to be factorized is `a^2 - 1 -2x - x^2`

Take common -1from the last three terms and then we have

 a² − 1 − 2x − x² ` = a^2 - (1 + 2x + x^3)`

 `=  a^2 - {(1)^2 + 2.1.x + (x)^2}`

` = a^2 - (1+x)^2`

` = (a)^2 - (1 + x)^2`

` = {a+ (1+x)}{ a-(1+x)}`

`= (a+1 + x)(a-1-x)`

` = (a+x+1)(a- x -1)`