Question

Factor the expression completely over the complex numbers: 25x2 +144

Answer 1

Answer:

25x² + 144 = (5x + 12i) (5x - 12i).

Step-by-step explanation:

We have to factorize the expression 25x² + 144, using the complex number.

Now, $i = \sqrt{- 1}$ can be treated as the complex number as there is negative value with in square root.

So, $i^{2} = - 1$

Therefore, we can write the original expression as  

25x² + 144

= 25x² - (i²)(144)  

= (5x)² - (12i)²

= (5x + 12i) (5x - 12i)

So, the factorization is 25x² + 144 = (5x + 12i) (5x - 12i). (Answer)