Factoring. (5) Page 600 #21 43 Right **********Quiz Tomorrow********** (10) Page #20 32 Right; #35 47 Right *****Quiz tomorrow****
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1 Algebra Unit 6: Factoring Name: Date: Period: # Factoring (1) Page 629 #6 8; #15 20 (2) Page 629 #21, 22, (3) Worksheet (4) Page 600 #19 42 Left (5) Page 600 #21 43 Right **********Quiz Tomorrow********** (6) Page 607 #5 8; #15 25 odd (7) Page 607 #12 14; Even, and LEFT (8) Page 614 #5 8; #18 30 left (9) Page #15 17 ; #19 31 Middle; #33 46 left (10) Page #20 32 Right; #35 47 Right *****Quiz tomorrow**** (11) Page 622 #18 48 left (12) Page 622 #20 50 right (13) Page 629 #23 28, (14) worksheet (15) Page 608 #63, 64; page 630 #55 57; page 637 #44, 45 (16) worksheet (17) Chapter review for test tomorrow (18) Page #9-17
2 10.8 GCF and Grouping (I,E/3) - Supplement Factor by Greatest Common Factor (aka GCF) and Factor by Grouping E1) Factor by GCF: 14x 4 21x 2 P1) Factor by GCF: 33x 5 121x 2 E2) Factor by Grouping: x 3 + 2x 2 +3x + 6 P2) Factor by Grouping: x 3 + 4x 2 + 6x + 24 E3) Factor Completely: 3m 3 15m 2 6m + 30 P3) Factor Completely: 2c 4 + 2c 3 24c 24
3 10.4 Solving Polynomial Equations in Factored Form (I, E/2) Solving Polynomial Equations in factored form by applying the Zero Product Property (ZPP) a b = 0 a = 0 OR b = 0 E1) Solve using the ZPP P1) Solve using the ZPP 3x(x + 7)(x 3) = 0 2y(y 8)(y + 2) = 0 E2) Solve using the ZPP P2) Solve using the ZPP 4(3x 2)(x + 4) = 0 7(2x + 3)(3x 2) = 0 E3) Solve using the ZPP P3) Solve using the Zpp (x 2)(x + 3) = 0 ( x 4)(x + 1) = 0 E4) Solve using the ZPP P4) Solve using the ZPP (x + 5) 2 = 0 (x + 8) 2 = 0 E5) Solve using the ZPP P5) Solve using the ZPP (2x + 1)(3x 2)(x 1) = 0 (3x 2)(4x + 3)(x + 4) = 0
4 10.5 Factor QT1 (x 2 +bx +c) and Solve Quadratics by Factoring (I, E/2) Factor Quadratic Trinomials with a leading coefficient of 1 (QT1) There are many ways to factor trinomials (i.e. Guess and Check, ac method and the X method). However, some polynomials cannot be factored. The Discriminant (b 2 4ac) can be used to determine if a trinomial can be factored. A quadratic trinomial can be factored (using integer coefficients) only if the Discriminant is a perfect square. E1) Factor QT1: x 2 + 3x + 2 P1) Factor QT1: x 2 + 8x + 15 E2) Factor QT1: x 2 5x + 6 P2) Factor QT1: x 2 9x + 20 E3) Factor QT1: x 2 2x 8 P3) Factor QT1: x 2 8x 9 E4) Factor QT1: x 2 + 7x 18 P4) Factor QT1: x 2 + 3x 18 E5) Factor QT1: x 2 + 3x 6 P5) Factor QT1: x 2 + 6x 5 E6) Factor Completely: 4x x x P6) Factor Completely: 5x 3 25x 2 30x E7) Solve by Factoring (ZPP) P7) Solve by Factoring (ZPP) x 2 3x = 10 x 2 5x = 24
5 10.6 Factor QT2 (ax 2 +bx +c) and Solve Quadratics by Factoring (I, E/3) Factor Quadratic Trinomials with a leading coefficient that is not 1 (QT2) There are many ways to factor trinomials (i.e. Guess and Check, ac method and the X method). However, some polynomials cannot be factored. The Discriminant (b 2 4ac) can be used to determine if a trinomial can be factored. A quadratic trinomial can be factored (using integer coefficients) only if the Discriminant is a perfect square. E1) Factor QT2: 2x x + 5 P1) Factor QT2: 3 x 2 + 5x + 2 E2) Factor QT2: 3x 2 4x 7 P2) Factor QT2: 2x x 11 E3) Factor QT2: 6x 2 19x + 15 P3) Factor QT2: 8x 2 14x 15 E4) Factor Completely: 6x 2 2x 8 P4) Factor Completely: 6x 2 + 9x 27 E6) Solve by Factoring (ZPP) P6) Solve by Factoring (ZPP) 21n n + 7 = 6n x x 11 = 12x + 10
6 10.7 Factor Special Products (DOTS and PST) and Solve Quadratics by Factoring (I, E/2) Factoring Difference of Two Squares (DOTS) and Perfect Square Trinomials (PST) Difference of Two Squares (DOTS) Perfect Square Trinomials (PST) a 2 b 2 Original 1. a 2 + 2ab + b 2 Original (a + b)(a b) Factored Form (a + b) 2 Factored Form 2. a 2 2ab + b 2 Original (a b) 2 Factored Form E1) Factor DOTS: P1) Factor DOTS: a. m 2 4 b. 4p 2 25 a. m 2 9 b. 49q 2 81 E2) Factor PST: P2) Factor PST: a. x 2 4x + 4 b. 16y y + 9 a. x 2 8x + 16 b. 9y y E3) Factor Completely: 50 98x 2 P3) Factor Completely: 12 27x 2 E4) Factor Completely: 3x 2 30x + 75 P4) Factor Completely: 2x 2 12x + 18 E5) Solve by Factoring (ZPP) P5) Solve by Factoring (ZPP) -2x x 18 = 0 8x 3 18x = 0 E6) Solve by Factoring (ZPP) P6) Solve by Factoring (ZPP) x 2 + x = 0 x2-2 3 x = 0
7 Factoring Application Problems (Area) (I,E/2)-Keystone Released E1) You are putting a stone border along two sides of a rectangular Japanese garden that measures 6 yards by 15 yards. Your budget limits you to only enough stone to cover 46 square yards. How wide should the border be? x 15 garden 6 stone x E2) An object lifted with a rope or wire should not weigh more than the safe working load for the rope or wire. The safe working load S (in pounds) for a natural fiber rope is a function of C, the circumference of the rope in inches. Safe working load model: 150 C 2 = S You are setting up a block and tackle to lift a 1350 pound safe. What size natural fiber rope do you need to have a safe working load? E3) The width of a box is 1 inch less than the length. The height is 4 inches greater than the length. The box has a volume of 12 cubic inches (V = l w h). What are the dimensions of the box?
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