$x^2 + 4x + 3 = (x + 1)(x + 3)$

$x^2 - 4x + 4 = (x - 2)(x - 2)$

$x^2 - 4 = (x + 2)(x - 2)$

$x^2 - 1 = (x^2 + 1)(x^2 - 1)$

$x^2 + 5x + 6 = (x + 3)(x + 2)$

$x^2 - x - 2 = (x + 2)(x - 2)$

$x^2 + 4x + 4 + x(x + 4)$

$x^2 - 2 = (x^2)(2) - (2)^2$

$x^2 - 4x + 9$