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To factor the given trinomial \( 11p^2q - 59pq^2 + 42pq^2 \), we will proceed as follows:

1. **Combine Like Terms:** First, let's ensure the terms are simplified. However, from the given trinomial, it seems the terms are already simplified.

   The trinomial is:
   \[
   11p^2q - 59pq^2 + 42pq^2
   \]

2. **Combine the \(pq^2\) Terms:**
   \[
   -59pq^2 + 42pq^2 = -17pq^2
   \]
   So, the trinomial simplifies to:
   \[
   11p^2q - 17pq^2
   \]

3. **Factor out the common factor:**
   The common factor in both terms is \(pq\). Therefore, we factor out \(pq\) from each term:
   \[
   pq(11p - 17q)
   \]

Thus, the factored form of the trinomial \( 11p^2q - 59pq^2 + 42pq^2 \) is:

\[
pq(11p - 17q)
\]

Would you like any further details on this factorization?

### Related Questions:
1. How do you factor a trinomial where the leading coefficient is greater than 1?
2. Can you explain how to recognize and factor common factors from a polynomial?
3. What is the difference between factoring and expanding a polynomial?
4. How would you factor a polynomial with four terms (e.g., by grouping)?
5. How does the distributive property relate to factoring?

### Tip:
Always start by looking for a common factor in all terms before attempting more complex factoring techniques.

Learn how to factor the trinomial 11p^2q - 59pq^2 + 42pq^2 step-by-step. This problem involves polynomial factorization and combining like terms, suitable for high school students.

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