Factor the polynomial 12x^3y^2-27x

Question

How do you factor this polynomial 

Answer 1

Find the common factor, and factor it out.

 

12x³y² - 27x = 2²3x³y² - 3³x = 3x(4x²y² - 9)

 

Note that

 

4x²y² - 9 = (2xy - 3)(2xy + 3).

 

i.e. a difference of squares.

 

12x³y² - 27x = 3x(2xy - 3)(2xy + 3)