1. **State the problem:** Factor the expression $$5y^2z - 42x^4y^5$$ completely. 2. **Identify common factors:** Look for the greatest common factor (GCF) in both terms. - The coefficients are 5 and 42. The GCF of 5 and 42 is 1. - For variables, both terms have at least $$y^2$$. 3. **Extract the GCF:** The GCF is $$y^2$$. 4. **Rewrite the expression factoring out $$y^2$$:** $$ 5y^2z - 42x^4y^5 = y^2(5z) - y^2(42x^4y^3) = y^2(5z - 42x^4y^3) $$ 5. **Check if the expression inside parentheses can be factored further:** - The terms inside parentheses, $$5z$$ and $$42x^4y^3$$, have no common factors. 6. **Final factored form:** $$ \boxed{y^2(5z - 42x^4y^3)} $$