Question

Factor the expression over the complex numbers x^2+20

Answer 1

Answer:

$(x - 2i\sqrt{5} )(x+2i\sqrt{5} )$

Step-by-step explanation:

To do that you need to use this:

$x^{2} -y^{2} =(x-y)(x+y)$

In order to do the substraction you need to put a minus to 20

$x^{2}+20 \\=x^{2} - (-20) \\=(x-\sqrt{-20} )(x+\sqrt{-20} ) \\=(x - 2i\sqrt{5} )(x+2i\sqrt{5} ); \\\\\\\sqrt{-20} =\sqrt{(-1)(2^{2})(5)} =2i\sqrt{5}$