The given polynomial is expressed as
x^2 - 15x + 36
We would apply the method of factorisation. We would find two terms such that their sum or difference is - 15x and their product is 36x^2. The terms are - 12x and - 3x. By replacing - 15x with these terms, we have
x^2 - 12x - 3x + 36
By factorising, we have
x(x - 12) - 3(x - 12)
Since x - 12 is common, we have
(x - 12)(x - 3)
The correct option is (x - 3)(x - 12)