1. **Problem Statement:** Factoring by grouping is a method used to factor polynomials with four or more terms by grouping terms with common factors. 2. **Formula and Rules:** The general idea is to group terms in pairs (or groups) and factor out the greatest common factor (GCF) from each group. Then, if the resulting binomials are the same, factor them out. 3. **Example 1:** Factor $x^3 + 3x^2 + 2x + 6$ - Group terms: $(x^3 + 3x^2) + (2x + 6)$ - Factor each group: $x^2(x + 3) + 2(x + 3)$ - Factor out common binomial: $(x + 3)(x^2 + 2)$ 4. **Example 2:** Factor $ab + ac + bd + cd$ - Group terms: $(ab + ac) + (bd + cd)$ - Factor each group: $a(b + c) + d(b + c)$ - Factor out common binomial: $(b + c)(a + d)$ 5. **Explanation:** Factoring by grouping works well when the polynomial can be split into groups that share a common binomial factor. This method simplifies complex polynomials into products of simpler expressions. 6. **Summary:** - Group terms in pairs. - Factor out the GCF from each group. - Factor out the common binomial. This method is especially useful for four-term polynomials and can sometimes be extended to more terms.