Answer
a) square is already completed; irreducible
b) square is already completed; factors as $(x-\sqrt 5)(x+\sqrt 5)$
c) $x^{2}+4x+6$ = $(x+2)^{2}+2$; irreductible
d) $x^{2}+4x+2$ = $(x+2)^{2}-2$; factors as $(x+2-\sqrt 2)(x+2+\sqrt 2)$
Work Step by Step
a) square is already completed; irreducible
b) square is already completed; factors as $(x-\sqrt 5)(x+\sqrt 5)$
c) $x^{2}+4x+6$ = $(x+2)^{2}+2$; irreductible
d) $x^{2}+4x+2$ = $(x+2)^{2}-2$; factors as $(x+2-\sqrt 2)(x+2+\sqrt 2)$
