1. **Stating the problem:** We want to learn how to factor algebraic expressions. Factoring means rewriting an expression as a product of simpler expressions. 2. **Formula and rules:** A common factoring technique is factoring quadratic expressions of the form $ax^2 + bx + c$ into $(mx + n)(px + q)$ where $m \times p = a$ and $n \times q = c$. 3. **Example:** Factor $6x^2 + 11x + 3$. 4. **Step 1: Multiply $a$ and $c$:** $$6 \times 3 = 18$$ 5. **Step 2: Find two numbers that multiply to 18 and add to $b=11$:** These numbers are 9 and 2 because $9 \times 2 = 18$ and $9 + 2 = 11$. 6. **Step 3: Rewrite the middle term using these numbers:** $$6x^2 + 9x + 2x + 3$$ 7. **Step 4: Group terms:** $$(6x^2 + 9x) + (2x + 3)$$ 8. **Step 5: Factor out the greatest common factor (GCF) from each group:** $$3x(2x + 3) + 1(2x + 3)$$ 9. **Step 6: Factor out the common binomial factor:** $$(3x + 1)(2x + 3)$$ 10. **Explanation:** We broke the middle term into two parts to create groups with common factors, then factored each group and finally factored out the common binomial. **Final answer:** $$6x^2 + 11x + 3 = (3x + 1)(2x + 3)$$