Respuesta :

claudettoterohil
Factor: 
3x^2 + 27
= 3(x^2  + 9)
Answer is 3(x^2 + 9), when factored.


A) (3x + 9i)(x + 3i)
= (3x + 9i)(x + 3i)
= (3x)(x) + (3x)(3i) + (9i)(x) + (9i)(3i)
= 3x^2 + 9ix + 9ix + 27i^2
= 27i^2 + 18ix + 3x^2



B) (3x - 9i)(x + 3i)
= (3x +  - 9i)(x + 3i)
= (3x)(x) + (3x)(3i) + ( - 9i)(x) + (- 9i)(3i)
= 3x^2 + 9ix - 9ix - 27i^2
= 27i^2 + 3x^2


C) (3x - 6i)(x + 21i)
= (3x +  - 6i)(x + 21i)
= (3x)(x) + (3x)(21i) + (- 6i)(x) + ( -6i)(21i)
= 3x^2 + 63ix - 6ix - 126i^2
=  - 126i^2 + 57ix + 3x^2






D) (3x - 9i)(x - 3i)
=  (3x +   - 9)(x +  - 3)
= (3x)(x) + (3x)( - 3i) + (- 9)(x) + ( - 9)( - 3i)
= 3x^2 - 9ix - 9x + 27i
= 9ix + 3x^2 + 27i - 9x









Hope that helps!!!

vijayhalder031

The correct answer is option B.

Concept:

  • Firstly, we will factorize the given expression.
  • We will expand each of the options and will match with the factorized expression.

How to solve the given question?

  • Factoring the given expression
    3x² + 27
    = 3(x²  + 9)
  • Option A :  (3x + 9i)(x + 3i)
    = (3x + 9i)(x + 3i)
    = (3x)(x) + (3x)(3i) + (9i)(x) + (9i)(3i)
    = 3x² + 9ix + 9ix + 27i²
    = 27i² + 18ix + 3x²
  • Option B: (3x - 9i)(x + 3i)
    = (3x +  - 9i)(x + 3i)
    = (3x)(x) + (3x)(3i) + ( - 9i)(x) + (- 9i)(3i)
    = 3x² + 9ix - 9ix - 27i²
    = 27i² + 3x²
  • Option C: (3x - 6i)(x + 21i)
    = (3x +  - 6i)(x + 21i)
    = (3x)(x) + (3x)(21i) + (- 6i)(x) + ( -6i)(21i)
    = 3x² + 63ix - 6ix - 126i²
    =  - 126i² + 57ix + 3x²
  • Option D: (3x - 9i)(x - 3i)
    =  (3x +   - 9)(x +  - 3)
    = (3x)(x) + (3x)( - 3i) + (- 9)(x) + ( - 9)( - 3i)
    = 3x² - 9ix - 9x + 27i
    = 9ix + 3x² + 27i - 9x

Thus, the correct answer is option B.

Learn more about factorization here:

https://brainly.com/question/723406

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