1. The problem: Understand the basic rules for factoring algebraic expressions. 2. Factoring is the process of breaking down an expression into simpler expressions (factors) that, when multiplied, give the original expression. 3. Common rules for factoring include: - **Greatest Common Factor (GCF):** Always look for the largest factor common to all terms. - **Factoring by grouping:** Group terms with common factors and factor each group. - **Factoring trinomials:** For expressions like $ax^2 + bx + c$, find two numbers that multiply to $ac$ and add to $b$. - **Difference of squares:** $a^2 - b^2 = (a - b)(a + b)$. - **Perfect square trinomials:** $a^2 \pm 2ab + b^2 = (a \pm b)^2$. - **Sum or difference of cubes:** $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ and $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$. 4. Example: Factor $6x^2 + 9x$. - Step 1: Find GCF of 6 and 9, which is 3. - Step 2: Factor out 3x: $6x^2 + 9x = 3x(2x + 3)$. 5. Factoring helps simplify expressions and solve equations by setting factors equal to zero. Understanding these rules allows you to factor most algebraic expressions efficiently.