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The expression is \( 3z^2 + 5z + 2 \). To factor this completely, we need to find two binomials that multiply to give this quadratic expression. 

The factorization of \( 3z^2 + 5z + 2 \) is:

\[
(3z + 2)(z + 1)
\]

This is the completely factored form of the given expression.

Would you like further explanation on how this was factored, or do you have any other questions?

Here are 5 related questions:
1. How do you factor quadratic expressions in general?
2. What are common factoring techniques for polynomials?
3. What is the quadratic formula and when is it used?
4. Can all quadratic expressions be factored?
5. How do you check if a factorization is correct?

**Tip:** Always verify your factorization by expanding the factors back to the original expression!

Factor the expression 3z^2 + 5z + 2 completely.

Learn how to factor the quadratic expression 3z^2 + 5z + 2 completely. This example covers key algebraic concepts, such as factoring quadratic expressions, suitable for students in Grades 8-10.

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