We are given two functions:

• $f(x) = x^2 + 5x + 6$
• $g(x) = x + 2$

We are asked to find $(f - g)(x)$, which means subtracting $g(x)$ from $f(x)$.

Step 1: Express the subtraction

$(f - g)(x) = f(x) - g(x)$

Substitute the given expressions for $f(x)$ and $g(x)$:

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

Step 2: Simplify the expression

Distribute the subtraction:

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

Now, combine like terms:

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

$(f - g)(x) = x^2 + 4x + 4$

Final Answer:

The result of $(f - g)(x)$ is:

$(f - g)(x) = x^2 + 4x + 4$

Would you like further clarification or more details on any part of the process?

Related Questions:

1. How do you find the difference between two functions algebraically?
2. What happens when you subtract a linear function from a quadratic one?
3. How would you factor the result $x^2 + 4x + 4$?
4. What does it mean to simplify a polynomial?
5. How can you find the sum of two polynomials?

Tip: Always ensure to combine like terms carefully when adding or subtracting polynomials!