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In Exercises 11-22, factor the polynomial completely. (See Example 2.) ER 11. 2r - 2r 12. 36a - 4a? 13. 22 - 7c + 19 14. m2 - Sm - 35 15. 6g - 24g2 + 24g 16. -15d + 21ď² – 6d 17. 3 + 3r - 90r³ 18. Sw- 40w3 + 80w² 3 19. -4c + 8 – 28 20. 8f + 81 - 72 21. -5-4b + 20 22. + 4 – 25h – 100 In Esercises 23-28, solve the equation. (See Example 3.)

In Exercises 11-22, factor the polynomial completely. (See Example 2.) ER 11. 2r - 2r 12. 36a - 4a? 13. 22 - 7c + 19 14. m2 - Sm - 35 15. 6g - 24g2 + 24g 16. -15d + 21ď² – 6d 17. 3 + 3r - 90r³ 18. Sw- 40w3 + 80w² 3 19. -4c + 8 – 28 20. 8f + 81 - 72 21. -5-4b + 20 22. + 4 – 25h – 100 In Esercises 23-28, solve the equation. (See Example 3.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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7.8 Exercises Dynamic Solutions available at BigideasMath.com -Vocabulary and Core Concept Check 1. VOCABULARY What does it mean for a polynomial to be factored completely? 2. WRITING Explain how to choose which terms to group together when factoring by grouping. Monitoring Progress and Modeling with Mathematics 32. In Exercises 3-10, factor the polynomial by grouping. (See Example 1.) 31. 3. + + 2x + 2 4. y - 9y? + y – 9 5. 32 + 22 – 122? – 8 6. 2s – 27 - 18s + 3s 7. + xy + 8x + 8y 8. q +q + 5pq + Sp 9. m? - 3m + mn – 3n 10. 2a? + 8ab – 3a – 12b y = -2x + 16x³ - 32x? 4x + 25x2 - 56x In Exercises 11-22, factor the polynomial completely. (See Example 2.) ERROR ANALYSIS In Exercises 33 and 34, describe and correct the error in factoring the polynomial completely. 11. 2r - 2x 12. 36a - 4a? 33. 13. 22 - 7c + 19 14. m² – Sm – 35 a + 8a? – 6a – 48 = a²(a + 8) + 6(a + 8) = (a + 8)(a² + 6) 15. 6g - 24g? + 24g 16. -15d + 21ď² – 6d 17. 3 +3r - 90r³ 18. Sw - 40w³ + 80w² 34. 19. -4c + 8ơ – 28 20. 8f + 81 – 72 x - 6x – 9x + 54 = x°(x- 6) – {x- 6) 22. + 4h – 25h – 100 = (x - 6Xx² – 9) 21. -5 - 4b + 20 In Esercises 23-28, solve the equation. (See Example 3.) 35. MODELING WITH MATHEMATICS You are building a birdhouse in the shape of a rectangular prism that has a volufne of 128 cubie inches. The dimensions of the birdhouse in terms of its width are shown. 23, Sn-30n? + 40n = 0 24. -100A 0 25. +4x+ 4 26. 21+2 - 144 = 0 27. 12s-3- 0 28. 4y-7y + 28 16y (w+ 4) in In Exercises 29-32, find the a-coordinates of the points where the graph crosses the a-axis, (See Example 4) a. Write a polynomial that represents the volume of the bardhouse. 29. 30. A What are the dimensions of the badhouse? y-x 3x-24x 45a 81x Section 7.8 Factoring Polynomials Completely 407
Transcribed Image Text:7.8 Exercises Dynamic Solutions available at BigideasMath.com -Vocabulary and Core Concept Check 1. VOCABULARY What does it mean for a polynomial to be factored completely? 2. WRITING Explain how to choose which terms to group together when factoring by grouping. Monitoring Progress and Modeling with Mathematics 32. In Exercises 3-10, factor the polynomial by grouping. (See Example 1.) 31. 3. + + 2x + 2 4. y - 9y? + y – 9 5. 32 + 22 – 122? – 8 6. 2s – 27 - 18s + 3s 7. + xy + 8x + 8y 8. q +q + 5pq + Sp 9. m? - 3m + mn – 3n 10. 2a? + 8ab – 3a – 12b y = -2x + 16x³ - 32x? 4x + 25x2 - 56x In Exercises 11-22, factor the polynomial completely. (See Example 2.) ERROR ANALYSIS In Exercises 33 and 34, describe and correct the error in factoring the polynomial completely. 11. 2r - 2x 12. 36a - 4a? 33. 13. 22 - 7c + 19 14. m² – Sm – 35 a + 8a? – 6a – 48 = a²(a + 8) + 6(a + 8) = (a + 8)(a² + 6) 15. 6g - 24g? + 24g 16. -15d + 21ď² – 6d 17. 3 +3r - 90r³ 18. Sw - 40w³ + 80w² 34. 19. -4c + 8ơ – 28 20. 8f + 81 – 72 x - 6x – 9x + 54 = x°(x- 6) – {x- 6) 22. + 4h – 25h – 100 = (x - 6Xx² – 9) 21. -5 - 4b + 20 In Esercises 23-28, solve the equation. (See Example 3.) 35. MODELING WITH MATHEMATICS You are building a birdhouse in the shape of a rectangular prism that has a volufne of 128 cubie inches. The dimensions of the birdhouse in terms of its width are shown. 23, Sn-30n? + 40n = 0 24. -100A 0 25. +4x+ 4 26. 21+2 - 144 = 0 27. 12s-3- 0 28. 4y-7y + 28 16y (w+ 4) in In Exercises 29-32, find the a-coordinates of the points where the graph crosses the a-axis, (See Example 4) a. Write a polynomial that represents the volume of the bardhouse. 29. 30. A What are the dimensions of the badhouse? y-x 3x-24x 45a 81x Section 7.8 Factoring Polynomials Completely 407
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