You have written the expression:

\[
\frac{x^2 + 5x + 12}{x + 1}
\]

Would you like to simplify this expression or are you looking for something specific, such as finding the quotient and remainder via polynomial division or perhaps analyzing the behavior of the function? Let me know how you'd like to proceed!

Here are five relevant questions:
1. Do you want to simplify the expression further?
2. Would you like to perform polynomial long division?
3. Are you looking for the roots of the numerator polynomial?
4. Would you like to explore any vertical or horizontal asymptotes of this rational function?
5. Would you like to analyze this function graphically?

**Tip:** When dividing polynomials, if the degree of the numerator is greater than or equal to the denominator, consider polynomial division for a simplified expression.

This problem explores simplifying and analyzing the rational function (x^2 + 5x + 12) / (x + 1) using polynomial division. Learn about quotient and remainder, vertical and horizontal asymptotes, and graph behavior. Suitable for students in Grades 10-12.

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