1. Factor and Solve Polynomial Equations 2.3 (GREEN book)

2. Vocabulary A factorable polynomial with integer coefficients is factored completely if it is written as a product of unfactorable polynomials with integer coefficients.

3. I. GCF - Always!! II. 2 Terms A. Difference of Squares a 2 – b 2 = _____________________________ B. Sum of Cubes a 3 + b 3 = _____________________________ C. Difference of Cubes a 3 – b 3 = ____________________________ III. 3 Terms A. Trinomial Square a. a 2 + 2ab + b 2 = __________________________ b. a 2 – 2ab + b 2 = __________________________ B. Plain Trinomial a. x 2 + bx + c ___________________ b. ax 2 + bx + c ___________________________ IV. 4 Terms - Grouping Factoring Quadratic Equations

4. Vocabulary For some polynomials you can factor by grouping pairs of terms that have a common monomial factor.

5. Example 1: Factor the polynomial completely 1. 4x 4 – 108x 2. 2b 3 + 16a 3

6. Example 2: Factor the polynomial x 3 + 2x 2 – x – 2 completely.

7. Example 3: Factor completely: 1. 3x 8 + 18x 5 + 24x 2 2. 81g 4 - 256

8. Example 4: Find the real-number solutions of the equation x 4 – 7x 2 = -12

9. Example 5. The dimensions (in inches) of a jewelry box are: length 4x, width (x – 1), and height (x – 2). If the volume of the box is 24 cubic inches, find the dimensions of the box.