Alg2 3.4 Notes.notebook

Alg2 3.4 Notes.notebook October 15, 2012Learning Targets:We are reviewing how to factor quadratic equationsWe will review the 6 different methods for factoringMethod 1: Taking out the common factorMethod 2: Factoring x 2 + bx +c by Product and Sum TableMethod 3: Factor by GroupingMethod 4: Factoring ax 2 + bx +c by Splitting the Middle TermMethod 5: Special Products - Difference of SquaresMethod 6: Special Product - Perfect Square Quadratic*Courtesy of Paul Sullivan(Method 1)Factoring by Taking out the common FactorSimplify7x 2 (2x 2 - 3)Factor14x 4 - 21x 22 7 x x x x - 3 7 x x2 7 x x x x - 3 7 x x7 x x (2 x x - 3)7x 2 (2x 2 - 3)

Alg2 3.4 Notes.notebook October 15, 2012(Method 4)Factoring ax 2 + bx + c by Splitting the Middle Term*British MethodEx 1: Factor 2x 2 + 11x + 5Producta cSumbStep by Step1. Make a Product and Sum Table theProduct has to be a c. The sum has tobe b.2.) Split the middle term to get fourterms.3.) Factor by groupingMore Examples1.) 3x 2 - 4x - 7Producta cSumbStep by Step1. Make a Product and Sum Table theProduct has to be a c. The sum has tobe b.2.) Split the middle term to get fourterms.3.) Factor by grouping2.) 6x 2 - 19x + 15

Alg2 3.4 Notes.notebook October 15, 2012These are examples of theFactoring Special Productstwo kinds of specialproductsWrite each expression in simplest form1.) (x + 4)(x - 4) 2.) (x + 7) 2 3.) (3x -5) 2Difference of Squares Pattern(Sum Special and Difference Products Pattern) Patterns (Short Cuts to FOIL)(a + b)(a - b) a 2 - bSum and Difference 2 Pattern (Difference of Squares)(a - b)(a + b) = a 2 - b 2Perfect Square Pattern(a + b) 2 = (a + b)(a + b) a 2 + 2ab + b 2Perfect Square Pattern (Square of a Binomial)(a + b) 2 = a 2 + 2ab + b 2(a - b) 2 = (a - b)(a - b) a 2 - 2ab + b(a - b) 22 = a 2 - 2ab + b 2(Method 5)Factor each difference of squares1.) m 2 - 25 2.) 4p 2 - 81 3.) 25 - 49x 2Press here for more practice problems4.) 49v 2 - 1444.) 81v 2 + 100

Alg2 3.4 Notes.notebook October 15, 2012(Method 6):Factor each Perfect Square Trinomial1.) x 2 + 16x + 64 2.) x 2 - 10x + 253.) 4x 2 + 36x + 81 4.) 9x 2 - 30x + 25Press here for more problems5.) x 2 - 14x + 49 6.) x 2 + 20x + 1007.) 49x 2 - 56x + 16 8.) 36x 2 + 60x + 253­4 Factoring PolynomialsUse the Factor Theorem to determine factors of apolynomial.Factor the sum and difference of two cubes.To find real roots of a polynomial.

Alg2 3.4 Notes.notebook October 15, 2012I. Factor Theorem1. Determine whether a linear binomial is a factor:A. (x + 1); (x 2 – 3x + 1) B. (x + 2); (3x 4 + 6x 3 – 5x – 10)II. Sum & Difference of Two Cubes2. Factor 125d 3 – 8(5d – 2)(25d 2 + 10d + 4)

Alg2 3.4 Notes.notebook October 15, 2012III. All together now...3. Factor (grouping):x 3 – x 2 – 25x + 25.4. Factor (cubic):4x 4 + 108x5. Factor (Quadratic):x 4 + 4x 2 ­ 453. (x – 1)(x – 5)(x + 5)4. 4x(x + 3)(x 2 – 3x + 9)5. (x 2 + 9)(x 2 ­ 5)IV. More Fun6. (Homework #28) Factor 24n 2 + 3n 57. x 4 ­ 14x 2 ­ 32Answers:6. 3n 2 (2 + n)(4 ­ 2n + n 2 )7. x 4 ­ 14x 2 ­ 32

Alg2 3.4 Notes.notebook October 15, 2012Say I knew(x ­ 7) was a factor of x 3 + 3x 2 + 2x ­ 504.How can a write the polynomial as a product?3­4 p.177#2, 3, 5, 7, 11, 15, 17, 19, 25, 27, 31, 36, 38,39, 41, 42, 51, 53, 54, 56, 57Check: SA11