[tex]a) {x}^{2} + 3x + 2[/tex]
[tex] = {x}^{2} + 2x + x + 2[/tex]
[tex] = x(x + 2) + 1(x + 2)[/tex]
[tex] = (x + 1)(x + 2)[/tex]
[tex]b) {x}^{2} + 5x + 6[/tex]
[tex] = {x}^{2} + 2x + 3x + 6[/tex]
[tex] = x(x + 2) + 3(x + 2)[/tex]
[tex] = (x + 2)(x + 3)[/tex]
[tex]c) {x}^{2} + 7x + 12[/tex]
[tex] = {x}^{2} + 3x + 4x + 12[/tex]
[tex] = x(x + 3) + 4(x + 3)[/tex]
[tex] = (x + 3)(x + 4)[/tex]