Question

Difference of Squares gives which complex factors for the expression x^2+11?

Answer 1

(x+i times the square root of 11)(x-i times the square root of 11)

Answer 2

The complex factor for the expression
`x^2+11` is,
`(x+i√(11))(x-i√(11))`.

Explanation:

Difference of squares states that it can be factored as follows:

`a^2-b^2 = (a+b)(a-b)`

Given the expression:

`x^2+11`

we can write above as;

`x^2+11 = x^2+(-1)(-11)` =
`x^2-(11)(i^2)` [ since, i is the imaginary ;
`i^2 = -1`]

`x^2+11 = x^2 -(i√(11))^2`

By definition of difference of squares:

`x^2 -(i √(11))^2 = (x+i√(11))(x+i√(11))`

⇒
`x^2+11 = (x+i√(11))(x-i√(11))`.