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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.

Given: f(x) = x² + 5x + 6 and h(x) = x + 2, solve (h - f)(x).

Learn how to subtract the functions f(x) = x² + 5x + 6 and h(x) = x + 2 to find (h - f)(x). This problem covers key algebraic concepts, such as function subtraction and polynomial operations. Suitable for students in Grades 9-10.

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