To find $(f-h)(x)$, we need to subtract $h(x)$ from $f(x)$:

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

Now, compute $(f-h)(x)$:

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

Distribute the subtraction: $(f-h)(x) = x^2 + 5x + 6 - x - 2$

Combine like terms: $(f-h)(x) = x^2 + 4x + 4$

So, $(f-h)(x) = x^2 + 4x + 4$.

Would you like any more details or have any questions?

Here are 5 related questions:

1. How do you find $(f \cdot h)(x)$ given the same functions?
2. What is the result of $(f + h)(x)$ for these functions?
3. How do you find $(f/h)(x)$ and what are the conditions for it to be defined?
4. What is the vertex of the quadratic function $(f-h)(x)$?
5. How do you find the roots of the equation $(f-h)(x) = 0$?

Tip: When subtracting polynomials, remember to distribute the negative sign to each term in the polynomial you are subtracting.