Answer:
The factor is (x+2).
Step-by-step explanation:
[tex]x^{2} +4x+4[/tex]
Lets assume this to be zero.
[tex]x^{2} +4x+4=0[/tex]
factoring it we get
[tex]x^{2} +2x+2x+4=0[/tex]
[tex]x(x+2)+2(x+2)=0[/tex]
This gives [tex](x+2)(x+2)[/tex] as factors.
Therefore, the factor is (x+2)
We can also check this as :
[tex](x+2)^{2} =x^{2} +4x+4[/tex]