Which of the followng best describes the relationship between (x-3) and the polynomial x^3+4x^2+2

The functions have the same end behavior.

Step-by-step explanation:

Upon a first glace, one relationship I can see between the two functions is their end behavior. For both functions:

as x ⇒ - ∞, f (x) ⇒ - ∞

as x ⇒ ∞, f (x) ⇒ ∞

this is because anytime a function's largest exponent is odd, it will have the same end behavior as a linear function, and anytime the exponent is even, it will have the same end behavior as a quadratic function.

Other than that, the functions may have similar x-intercepts, but I do not believe that is the case. They definitely have different y-intercepts.