2x - 3y is a factor of?

4x² + 2x - 3y + 9y² - 12xy

Here, check from options, we have option 4 as:

⇒ 4x² + 2x - 3y + 9y² - 12xy

we can write it as:

⇒ (2x)² + (2x - 3y) + (3y)² - 2(2)(3)xy

⇒ [(2x)² + (3y)² - 2(2)(3)xy] + (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.