2x - 3y is a factor of?

4x² + 2x - 3y + 9y² - 12xy

The correct answer is Option 4: 4x² + 2x - 3y + 9y² - 12xy

 4x² + 2x - 3y + 9y² - 12xy

we can write it as:

⇒ 4x² - 12xy + 9y² + 2x - 3y 

 ⇒  (4x² - 12xy + 9y² + (2x - 3y)

⇒ (2x - 3y)² + (2x - 3y)

Take 2x - 3y common, we get

⇒ (2x - 3y){2x - 3y + 1}

Here, 2x - 3y is the factor. Hence, option 4 is right answer.