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The expression to simplify is:

\[
\frac{4z^3 + 2z^2}{2}
\]

We can simplify this by factoring out the common terms:

1. Factor the numerator:

\[
4z^3 + 2z^2 = 2(2z^3 + z^2)
\]

2. Now, divide the entire expression by 2:

\[
\frac{2(2z^3 + z^2)}{2} = 2z^3 + z^2
\]

Thus, the simplified expression is:

\[
2z^3 + z^2
\]

Would you like more details, or do you have any questions?

Here are five related questions to expand on this topic:
1. How do you factor polynomials with multiple terms?
2. What are the common methods for simplifying algebraic fractions?
3. How would you simplify the expression if the denominator was something more complex?
4. What happens when you divide powers of variables with the same base?
5. Can this method be applied to simplify more complex polynomial fractions?

**Tip**: Always look for common factors in both the numerator and denominator to simplify algebraic fractions efficiently.

This guide simplifies the polynomial expression (4z^3 + 2z^2) / 2 using factoring and division techniques. Learn step-by-step to simplify expressions involving powers and polynomials. Ideal for students in Grades 8-10.

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