Question

Factor the expression over the complex numbers. x^2 +20 Enter your answer in the box.

Answer 1

Answer:

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

Step-by-step explanation:

Let solve this first:

$x^2 + 20 = 0\\x^2 = -20\\x = \sqrt{-20} \\x=\sqrt{20}i$

Note: i = √-1

Using the property of radicals [√a√b=√(ab)], we can write √20 as:

√20 = √4√5 = 2√5

We can write:

x = ± 2√5 i

If we take the two roots (answers) as -a, and a, then we can write the factorization as:

(x - a ) (x + a)

Thus this factorization is:

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