1. **State the problem:** Find the greatest common factor (GCF) of the polynomial expression $15x^2y - 10xy^3$. 2. **Recall the formula and rules:** The GCF of terms is the product of the greatest common factors of their coefficients and the lowest powers of common variables. 3. **Find the GCF of coefficients:** - Coefficients are 15 and 10. - The GCF of 15 and 10 is 5. 4. **Find the GCF of variables:** - Variables in first term: $x^2 y$ - Variables in second term: $x y^3$ - Common variables are $x$ and $y$. - Take the lowest powers: $x^{\min(2,1)} = x^1 = x$, $y^{\min(1,3)} = y^1 = y$. 5. **Combine GCF:** - GCF = $5xy$ 6. **Factor out the GCF:** $$15x^2y - 10xy^3 = 5xy(\cancel{3x} - \cancel{2y^2})$$ 7. **Final answer:** $$\boxed{5xy(3x - 2y^2)}$$