1. Let's start by stating the problem: You want to know about factoring and the different ways to factor expressions. 2. Factoring is the process of breaking down an expression into simpler expressions (called factors) that, when multiplied together, give the original expression. 3. There are several common methods to factor expressions: - **Factoring out the Greatest Common Factor (GCF):** Find the largest factor common to all terms and factor it out. - **Factoring by Grouping:** Group terms in pairs or sets and factor each group, then factor the common binomial. - **Factoring Trinomials:** For quadratics like $ax^2 + bx + c$, find two numbers that multiply to $ac$ and add to $b$, then split the middle term and factor by grouping. - **Difference of Squares:** Expressions like $a^2 - b^2$ factor as $(a - b)(a + b)$. - **Perfect Square Trinomials:** Expressions like $a^2 \pm 2ab + b^2$ factor as $(a \pm b)^2$. - **Sum or Difference of Cubes:** Expressions like $a^3 \pm b^3$ factor as $(a \pm b)(a^2 \mp ab + b^2)$. 4. Important rules: - Always look for the GCF first. - Recognize special patterns like difference of squares or perfect squares. - For trinomials, the leading coefficient $a$ affects the factoring method. 5. Example: Factor $6x^2 + 11x + 3$. - Multiply $a$ and $c$: $6 \times 3 = 18$. - Find two numbers that multiply to 18 and add to 11: 9 and 2. - Rewrite middle term: $6x^2 + 9x + 2x + 3$. - Group: $(6x^2 + 9x) + (2x + 3)$. - Factor each group: $3x(2x + 3) + 1(2x + 3)$. - Factor out common binomial: $(3x + 1)(2x + 3)$. 6. So, there are multiple ways to factor depending on the expression type, and mastering these methods helps simplify and solve equations effectively.