1. **Problem:** Factor out the GCF from $14r^2s^3 + 20r^3s - 10r^4s^5$. 2. **Step 1:** Identify the GCF of the coefficients: GCF of 14, 20, and 10 is 2. 3. **Step 2:** Identify the GCF of the variables: - For $r^2$, $r^3$, and $r^4$, the smallest power is $r^2$. - For $s^3$, $s$, and $s^5$, the smallest power is $s$. 4. **Step 3:** So, the GCF is $2r^2s$. 5. **Step 4:** Factor out $2r^2s$: $$14r^2s^3 + 20r^3s - 10r^4s^5 = 2r^2s(\cancel{7}s^2 + \cancel{10}r - \cancel{5}r^2s^4)$$ 6. **Step 5:** Simplify inside the parentheses: $$= 2r^2s(7s^2 + 10r - 5r^2s^4)$$ --- 7. **Problem:** Factor out the GCF from $15x^2y - 60x^3y^2$. 8. **Step 1:** GCF of coefficients 15 and 60 is 15. 9. **Step 2:** For variables: - $x^2$ and $x^3$, smallest power is $x^2$. - $y$ and $y^2$, smallest power is $y$. 10. **Step 3:** GCF is $15x^2y$. 11. **Step 4:** Factor out $15x^2y$: $$15x^2y - 60x^3y^2 = 15x^2y(\cancel{1} - \cancel{4}xy)$$ 12. **Step 5:** Simplify inside parentheses: $$= 15x^2y(1 - 4xy)$$ --- 13. **Problem:** Factor out the GCF from $6abc - 27ab^3 + 51ab t^2$. 14. **Step 1:** GCF of coefficients 6, 27, and 51 is 3. 15. **Step 2:** For variables: - $a$ is common in all terms. - $b$ is common in all terms. - $c$, $b^3$, and $t^2$ vary, so no common variable beyond $ab$. 16. **Step 3:** GCF is $3ab$. 17. **Step 4:** Factor out $3ab$: $$6abc - 27ab^3 + 51ab t^2 = 3ab(\cancel{2}c - \cancel{9}b^2 + \cancel{17}t^2)$$ 18. **Step 5:** Simplify inside parentheses: $$= 3ab(2c - 9b^2 + 17t^2)$$ --- **Final answers:** 1. $2r^2s(7s^2 + 10r - 5r^2s^4)$ 2. $15x^2y(1 - 4xy)$ 3. $3ab(2c - 9b^2 + 17t^2)$