Lesson 6 2 Reviewing Multiplying Polynomials Multiplying two

Lesson 6. 2: Reviewing Multiplying Polynomials Multiplying two polynomials: FOIL/Distributive Property

Special Products Product of two binomial conjugates (Difference of Squares Pattern) Square of a binomial (Perfect Square Trinomial Pattern)

Examples Multiply the following: 1. (2 x + 7)(2 x-7) 2. (3 – 5 x)(4 x + 2) 3. (7 x – 3)2

Lesson 6. 4: Factoring Polynomials Factoring out greatest common factors: This is typically the first step in factoring a polynomial. Sometimes it may be the only step. Ex. 3 x 2 – 15 x = 3 x(x – 5) Ex. 5 x 2 – 20 x – 60 = 5(x 2 – 4 x – 12)= 5(x – 6)(x + 2) Ex. 3 x 2 + 10 x – 8 = (3 x – 2)(x + 4)

Factoring Using Special Patterns Difference of Squares Pattern: Perfect Square Trinomial Pattern:

Examples Factor the following: 1. 4 x 2 – 36 y 2 2. x 2 – 14 x + 49 3. 12 x 2 + 60 x + 75

Two More Special Factoring Patterns Sum of Two Cubes Pattern: a 3 + b 3 = (a + b)(a 2 – ab + b 2) Ex. 8 x 3 + 27 = (2 x + 3)(4 x 2 – 6 x + 9) Difference of Two Cubes Pattern: a 3 – b 3 = (a – b)(a 2 + ab + b 2) Ex. 27 x 3 – 125 y 3 = (3 x – 5 y)(9 x 2 + 15 xy + 25 y 2)

Factoring by Grouping Group terms together and factor out common factors from each group. If these two new products have a common factor, factor out the common factor to complete the factoring by grouping. Ex. 3 x 2 + 6 x – 5 x – 10 = (3 x 2 + 6 x) + (-5 x – 10) = 3 x(x + 2) – 5(x + 2) = (x + 2)(3 x – 5)

Irreducible polynomials If a polynomial cannot be factored it is called irreducible. Ex. 3 x – 7 Ex. x 2 – x + 3