The expression \(\frac{X^3 + 3X^4}{X^2 + 16}\) cannot be simplified directly in the same manner as the previous one because the denominator \(X^2 + 16\) is a binomial. However, we can analyze the expression and discuss potential factorizations or simplifications.

### Steps:
1. **Look for common factors**: 
   The numerator \(X^3 + 3X^4 = X^3(1 + 3X)\), but the denominator \(X^2 + 16\) doesn't have any factors in common with the numerator. Hence, we cannot cancel any terms.

2. **Simplify if possible**: 
   There is no way to further simplify this expression by factoring, so the expression remains:
   \[
   \frac{X^3 + 3X^4}{X^2 + 16}
   \]

Unless you're performing a specific operation like long division, partial fraction decomposition, or further transformations, this is the simplest form of the expression.

Would you like to explore other ways to work with this expression, such as factoring or solving for particular values of \(X\)?

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Here are 5 related questions to consider:
1. How would you factor the numerator \(X^3 + 3X^4\)?
2. Can the denominator \(X^2 + 16\) be factored using complex numbers?
3. How would this expression change if the powers of \(X\) in the numerator were different?
4. What happens when you substitute specific values for \(X\) in this expression?
5. Can you apply polynomial division to this expression?

**Tip:** If you can't simplify an expression immediately, look for other strategies like polynomial division or substitutions to explore further.

Learn how to simplify the rational expression (X^3 + 3X^4) / (X^2 + 16) step-by-step. This problem involves polynomial division and rational expression simplification, suitable for advanced high school students.

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