Take out a common factor
First find the greatest factor shared by every term. Taking it outside the brackets makes the remaining expression easier to recognize.
6x² + 9x = 3x(2x + 3).
Look for a difference of squares
A squared quantity minus another squared quantity factors into a difference multiplied by a sum.
a² − b² = (a − b)(a + b), so x² − 16 = (x − 4)(x + 4).
Factor a monic quadratic
For x² + bx + c, find two numbers whose sum is b and whose product is c.
x² + 5x + 6 = (x + 2)(x + 3), because 2 + 3 = 5 and 2 × 3 = 6.