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 494 14-26 even p 501 1-18 even, 44, 46

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

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 + 36 Ex 2) 9x² - 6x + 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.

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

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

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)

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

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

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