1. **Problem:** Do a factoring example. 2. **Formula used:** A common factoring pattern is the greatest common factor rule: $$ab+ac=a(b+c)$$ This means we look for the biggest factor shared by every term. 3. **Example:** Factor $6x+12$. 4. **Find the greatest common factor:** Both $6x$ and $12$ share a factor of $6$. 5. **Rewrite each term using $6$:** $$6x+12=6x+6\cdot 2$$ 6. **Factor out the common factor:** $$6x+12=6(x+2)$$ 7. **Check the work:** Multiply back to make sure it matches the original expression. $$6(x+2)=6x+12$$ So the factoring is correct. 8. **Final answer:** $$6(x+2)$$