Question

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

Answer 1

25x² + 144 = (5x + 12i) (5x - 12i).

Explanation:

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

Now,
`i = √(- 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)