The expression \(\frac{X^3 + 3X^4}{X^2} + 16\) can be simplified step by step:

1. **Break up the fraction**:
   \[
   \frac{X^3 + 3X^4}{X^2} = \frac{X^3}{X^2} + \frac{3X^4}{X^2}
   \]

2. **Simplify each term**:
   - \(\frac{X^3}{X^2} = X\)
   - \(\frac{3X^4}{X^2} = 3X^2\)

3. **Combine the simplified terms**:
   \[
   X + 3X^2
   \]

4. **Add the constant term** \(16\) at the end:
   \[
   X + 3X^2 + 16
   \]

So, the simplified expression is:
\[
3X^2 + X + 16
\]

Would you like any more details or further explanation on this process?

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Here are 5 related questions to consider:
1. How would you factor the expression \(3X^2 + X + 16\) if needed?
2. What happens if the numerator is different, say \(X^3 + 4X^4\)?
3. How would the process change if the denominator was \(X^3\) instead of \(X^2\)?
4. What is the significance of each term in the quadratic expression \(3X^2 + X + 16\)?
5. How would this expression change if it were divided by a different monomial?

**Tip:** Always simplify terms individually when dividing expressions to make the process clearer and more manageable.

Learn how to simplify the fraction expression (X^3 + 3X^4) / X^2 + 16 with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomial division and fraction simplification. Suitable for students in Grades 7-9.

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