[tex] {x}^{2} + 5x + 6 = {x}^{2} + 2x + 3x + 6 = x( \frac{ {x}^{2} }{x} + \frac{2x}{x}) + 3( \frac{3x}{3} + \frac{2 \times 3}{3}) = x( {x}^{2 - 1} + 2) + 3(x + 2) = x(x + 2) + 3(x + 2) = (x + 2)( \frac{x(x + 2)}{x + 2} + \frac{3(x + 2)}{x + 2}) = (x + 2)(x + 3) [/tex]
