x + 2sqrt(x ^ 3 + 3x ^ 2 + 5x + 6)

Answer 1

You posed no question, so the only thing I notice is that
x^3 + 3x^2 + 5x + 6 = (x+2)(x^2 + x + 2)

we could write x + 2√( (x ^ 3 + 3x ^ 2 + 5x + 6) ) as
(x+2) + (x+2)^(1/2) * (x^2 + x + 2)^(1/2)
and then factor out √(x+2) as ...
(x+2)^(1/2) [ (x+2)^(1/2) + (x^2 + x + 2)^(1/2) ]

but we would be "complicating" this instead of simplifying.

Answer 2

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