1. Lesson 7-5 Factoring Special Products Lesson 7-6 Choosing a Factoring Method
Obj: The student will be able to 1) Factor perfect square trinomials 2) Factor the difference of two squares 1) Choose an appropriate method for factoring a polynomial 2) Combine methods for factoring a polynomial HWK: p even p even, 44, 46

2. Special Products
Perfect Square Trinomials Difference of Two Squares (a + b)² = a² + 2ab + b² (a + b)(a – b) = a² - b² (a – b)² = a² - 2ab + b²

3. Determine whether the trinomial is a perfect square. If so factor
Determine whether the trinomial is a perfect square. If so factor. If not, explain.
Ex 1) x² + 12x Ex 2) 9x² - 6x + 4

4. Ex 5) A company produces square sheets of aluminum, each of which has an area of (9x² + 6x + 1) m². Find an expression in terms of x for the perimeter of a sheet of aluminum. Then find the perimeter when x = 3m.

5. Determine whether the trinomial is a difference of two squares
Determine whether the trinomial is a difference of two squares. If so, factor. If not, explain.
Ex 6) x⁶ - 7y² Ex 7) 9p⁸ - 49p⁶

6. Methods to Factor Polynomials
Type of Polynomial
Way to factor
Any polynomial
Look for greatest common factor
Binomials
Look for difference of two squares
Trinomials
Look for perfect square trinomials or other factorable trinomials
Polynomials of four or more terms
Factor by grouping

7. Ex 1) 2x(x² + 16) Ex 2) (4x + 4)(x + 1)
Determine whether each expression is completely factored. If not, factor it.
Ex 1) 2x(x² + 16) Ex 2) (4x + 4)(x + 1)

8. Factor each polynomial completely
Ex 3) 4x³ + 16x² + 16x Ex 4) 2x²y – 2y³

9. Ex 5) -2xy² + 16xy – 32x Ex 6) 9q⁶ + 30q⁵ + 24q⁴

10. Ex 7) 2p⁵ + 10 p⁴ - 12p³ Ex 8) 2x² + 5x + 4