1. **Problem statement:** Factorize the expressions by factoring out the greatest common factor (GCF). 2. **Formula and rules:** To factor out the GCF, find the largest factor common to all terms and write the expression as the product of the GCF and the remaining terms. 3. **First expression:** $6g + 21h - 15$ - Find GCF of coefficients: GCF of 6, 21, and 15 is 3. - Factor out 3: $$6g + 21h - 15 = 3 \times 2g + 3 \times 7h - 3 \times 5$$ - Write as product: $$= 3(2g + 7h - 5)$$ 4. **Second expression:** $5j^3 - 20i^2k + 45ik^2$ - Find GCF of coefficients: GCF of 5, 20, and 45 is 5. - Variables common to all terms: None (since $j^3$, $i^2k$, and $ik^2$ share no common variable). - Factor out 5: $$5j^3 - 20i^2k + 45ik^2 = 5 \times j^3 - 5 \times 4i^2k + 5 \times 9ik^2$$ - Write as product: $$= 5(j^3 - 4i^2k + 9ik^2)$$ **Final answers:** - $6g + 21h - 15 = 3(2g + 7h - 5)$ - $5j^3 - 20i^2k + 45ik^2 = 5(j^3 - 4i^2k + 9ik^2)$