Mathematics: Difference of squares gives which complex factors for the expression x^2+11?

Difference of squares gives which complex factors

lIechonoxIl

16.06.2020

The complex factor for the expression x^2+11 is, $(x+i\sqrt{11})(x-i\sqrt{11})$ .

Step-by-step 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 ]

$x^2+11 = x^2 -(i\sqrt{11})^2$

By definition of difference of squares:

$x^2 -(i \sqrt{11})^2 = (x+i\sqrt{11})(x+i\sqrt{11})$

⇒ $x^2+11 = (x+i\sqrt{11})(x-i\sqrt{11})$ .

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