The expression you have provided is $(h - f)(x)$, where $f(x)$ and $h(x)$ are given as:

$f(x) = x^2 + 5x + 6$ $h(x) = x + 2$

To solve $(h - f)(x)$, we subtract the function $f(x)$ from $h(x)$.

$(h - f)(x) = h(x) - f(x)$

Substituting the given functions:

$(h - f)(x) = (x + 2) - (x^2 + 5x + 6)$

Now, distribute the negative sign through the second function:

$(h - f)(x) = x + 2 - x^2 - 5x - 6$

Combine like terms:

$(h - f)(x) = -x^2 + (x - 5x) + (2 - 6)$

$(h - f)(x) = -x^2 - 4x - 4$

So the final result is:

$(h - f)(x) = -x^2 - 4x - 4$

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

1. How would you find $(h + f)(x)$ using the same functions?
2. What is the graph of the function $(h - f)(x)$?
3. How do you find the roots of the equation $(h - f)(x) = 0$?
4. Can you calculate $(h \times f)(x)$ for the given functions?
5. What are the critical points of the function $(h - f)(x)$?

Tip: When subtracting polynomial functions, always ensure you distribute the negative sign across all terms of the function being subtracted.