To factor the expression \( 5y^2z - 42x^4y^5 \), let's follow the steps:

### Expression:
\[
5y^2z - 42x^4y^5
\]

### Step 1: Find the common factors

1. **Numerical coefficients**: The greatest common factor (GCF) of 5 and 42 is 1 (since 5 and 42 have no common factors other than 1).
   
2. **Variable \( y \)**: The lowest power of \( y \) is \( y^2 \) (since the terms have \( y^2 \) and \( y^5 \)).
   
3. **Variable \( z \)** and \( x \)**: There is no common factor between \( z \) and \( x^4 \).

### Step 2: Factor out the common terms

The common factor between the two terms is \( y^2 \).

\[
y^2(5z - 42x^4y^3)
\]

### Final factored expression:

\[
y^2(5z - 42x^4y^3)
\]

Let me know if you'd like further details or explanations.

### Relative Questions:
1. What is the process of finding the greatest common factor?
2. How do you factor polynomials with multiple variables?
3. Can you factor expressions with more complex terms?
4. What are the rules for factoring when coefficients are fractions?
5. How do you simplify expressions with exponents during factoring?

**Tip**: Always check for both numerical and variable common factors when factoring.

Learn how to factor the expression 5y^2z - 42x^4y^5 with a detailed step-by-step solution. This problem covers algebraic concepts including polynomials and factorization. Suitable for high school students.

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