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Name ________________________________________ Date __________________ Class__________________ LESSON 14-2 Practice B Factoring ax2 bx c Factor each trinomial. 1. 2x2 13x 15 2. 3x2 ________________________ 4. 5x2 21x ________________________ 7. 7x2 59x 24 11x 13 8. 3x2 29x 12 11. 3x2 7x 12 14. 11x2 12x2 35x 18 ________________________ 15 9. 8x2 2x 12. 2x2 16 25x 24 17. 9x2 49x 30 20x2 29x 6 _________________________ 22. The area of a rectangle is 20x2 27x 8. The length is 4x 1. What is the width? 20 73x 9 17x 30 ________________________ 15. 9x2 3x 2 ________________________ 18. 6x2 _________________________ 20. 23x ________________________ _________________________ ________________________ 19. 14x 27 ________________________ _________________________ ________________________ 16. 12x2 6. 6x2 7 _________________________ ________________________ 13. 8x2 11x 24x ________________________ ________________________ ________________________ 10. 2x2 3. 4x2 8 _________________________ 5. 4x2 4 10x x 40 ________________________ 21. 2x2 5x 42 ________________________ _________________________ © Houghton Mifflin Harcourt Publishing Company 386 Holt McDougal Analytic Geometry 6. Problem Solving 20; 1 Sum 1. x 1 and 20 19 2. rug: (x 5)(x 4); wall: (x 2)(x 15); rug: 16 ft by 25 ft, wall: 22 ft by 35 ft 2 and 10 8 Factors 4 and (x 7. 4)(x 5 3. a. x 5 b. 12 in. by 19 in. c. x2 x 12 1 4. D 5) Factors Sum 1 and 4 3)(x 6) 10. (x 5)(x 9) Reading Strategies 3 2 and 2 1)(x 4) 8. (x 0 9. (x 7)(x 2) 1 2 1 3 1 1 2 3 1 3 3. 6 x 1 3 2 3 1 2 1 3 2 2 3 2 2 3 2 x 1 2 3 x 6. 28 x 7. 6 x 8. 12 x x 1 7 x 4 3 5 3 x x 3. ; 4. : 5. ; 6. ; 7. ; 8. ; 9. ; 8)(x 3) 10. (x 3)(x 7) 12. (x 6)(x 5) 6x 2 3x 6x 2 5x 1 2x 1 1 3 3)(2x 5) 4. (3x 2)(2x 5) 6. (2x 3)(4x 1) 8. (3x 7)(3x 2) 1)(4x 7. (4x 1)(x 9. (3x 5)(2x 5) 10. (5x 2)(x 11. (7x 5)(3x 1) 12. (4x 3)(3x 13. (5x 9)(2x 1) 14. (3x 4)(x 1) 16. (4x 3)(x 3) 18. (3x 4)(2x 15. (x 2)(5x 17. (2x 19. (5x 1)(2x 2 48x 4) 2. (2x 5. (2x 7) 8) 3) 7) 27); (5x 20. 1 (2x 1)(3x 4) 21. 1(5x 2)(4x 3) 3)(x 9) 22. 4x 1 4) 4) 5) Practice B 1 4 2. (3x 4)(x 2) 4. (5x 1)(x 4) 1) 6. (3x 4)(2x 3)(x 8) 8. (3x 5)(x 9. (8x 1)(x 9) 10. (2x 13)(x 1) 11. (3x 8)(x 2) 12. (x 10)(2x 3) 13. (x 4)(8x 3) 14. (x 3)(11x 8) 16. (4x 3)(3x 4) 5 2 7 4 2) c 5)(x 1 3 4. Yes; the given polynomial expression is written as a product of polynomials of lower degree. There is no requirement that the coefficients be integers. 1 5 ; 3. (3x 5 6 (2 x 1)(3 x 1) 5. 15 x 2. Practice A 1. 1; (x 3)(5x 1 , 6 1 3 x ; 14-2 FACTORING ax2 bx 1. Distributive Property 1 2 1. 11. (x Challenge 2. 5. J 6. B 4; 3 (x 8m 1. (2x 3)(x 3. (2x 9)(2x 5. (4x 7)(x 7. (7x 15. (3x 1)(3x 5) 3) 2) 5) 3) © Houghton Mifflin Harcourt Publishing Company A72 Holt McDougal Analytic Geometry 17. (9x 5)(x 6) 18. (3x 19. 1(4x 9)(3x 20. 1(5x 21. 1(2x 6)(4x 1) 7)(x 6) 22. 5x Problem Solving 1. (x 3) cm 2. 1)(8c 5. (6m 1) 2. (7x 3)(2x 3) 5) 4. (4b 5)(5b 1) 6. (2x 7)(3x 4) 5)(2m 7. 1(5x 9. (5f 1(4t 4)(4t 1) or 4(4t 1)(t 1); 0 feet 3. (3x 8 3. (2c 5) 3)(4x 9)(3f 11. (15a 9) 8)(a 1(2x 7)(4t 10. (16h 50)(2x 15. (3k 4)(3k 17. (7x 4)(3x 5. C 6. F 7. B 8. G Reading Strategies 7) 5)(4h 3) 1. 1 3 2. 1 12; 2 6; 3 4 5) 3) 14. (4x 5)(x 2) 16. (8n 11)(3n 4) 18. (6p 7)(3p 25)(w 3) ft; increase of 2 ft 4. length increased by 5 ft, width increased by 7 ft 4) 9)(2x 1(13w 8. (t 2) 13. (3x 19. 5) 2) Practice C 1. (3d 7)(2d 12. 8)(2x 3. minus, minus 2) 4. ( 2) x )( x ) 5. Possible answer: 2) 1) ( x )( x ) Outer 20. (12x 5)(x 6) 3 1 1 12 3 21. (3y 1)(4y 15) 3 12 1 Inner 12 1 1 37 No 1 3 1 12 1 15 No 22. 4x 5 3 4 1 3 3 3 4 1 13 No 23. 2x 9 inches 3 3 1 4 3 4 3 1 15 No 3 6 1 2 3 2 6 1 12 No 3 2 1 6 3 6 2 1 20 Yes Review for Mastery 1. Factors Factors 1; 5 1; 4 1; 4; 5; 1; 9 1; 5 4; 1 1; 1; 5; 4; 21 1; 5 2; 2 1; 2; 5; 2; 12 (x Outer Inner 6. (3x 2)(x 6) 14-3 FACTORING SPECIAL PRODUCTS Practice A 2)(5x 2) 1. 5; x; 5 2. (3x 4)(x 1) 2. 1; 3x; 3x; 1; 3x; 2; 1 3. (2x 7)(x 3) 4. (2x 3)(2x 5. (3x 5)(x 4) 6. (5x 1)(x 7. 1(2x 5)(x 1) 3. (x 7) 6. 12x Challenge 7 15 12 15 4 5 0 3. (6x 1) 5. (x 1)(x 6. (x 4)(2x 2. 3 3 4. (8x 3)(x 1)(x 4. (6x 2)2 5. 6 is not a perfect square 1) 1. 4 9)2 2(2x 6). 7. a. x 4 in. b. 4(x 4) in. c. 48 in. 4 32 12 32 8 0 8. 3; 3 10. (t 5) 3 9. 2p; 7; 2p; 7 12)(t 3 12) 11. (4x5 y)(4x5 y) 5) 5) © Houghton Mifflin Harcourt Publishing Company A73 Holt McDougal Analytic Geometry