Question

Factor the expression over the complex numbers.


x2+50

Answer 1

Answer:

(x + 5√2 i) (x - 5√2 i)

Step-by-step explanation:

Now, x^2 + 50

= x^2 - (- 50)

= x^2 - 50i^2

= x^2 - (i 5√2)^2

= (x + 5√2 i) (x - 5√2 i) ,

which is the required factorization.

Remark:

We know that i = √(- 1). In this problem, 50 can be expressed as (- 50i^2). Then we apply the formula a^2 - b^2 = (a + b) (a - b)

Some homeworks for you:

1. p^2 + q^2

2. (a - b)^2 - 3^2

3. a^2 + 2a + 3