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For Exercises 9–22, use long division to divide. 9. (3x - 11r - 10) (x – 4)

For Exercises 9–22, use long division to divide. 9. (3x - 11r - 10) (x – 4)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I need help to do question 9, 13, 17, 19, and question 43 on section 2.3.

Chapter 2 Poly 280 3. -4 25.-4 -2 -25 4. 24 1 -4 1-6 28. (6x+25x - 19) ÷ (x + 5) 30. (2x2 + x- 21) (x - 3) (x + 1) 27. (4x + 15x + 1) + (* + 6) 29. (5x-17x-12) (*-4) 31. (4-&r-3-Sr) (+2) 4x-25-58e+ 232+198x-63 21+13x-3x' – 58x – 20x + 24 34. 32. (-5+ 2x + 5x- 2x) | X - 2 x-81 36. x + 3 33. 1-3 2+32 35. よ+2 38. (-5x – 18r + 63x + 128x 60) ÷ 37. (2x- 7- 56x+ 37x + 84) (*- 2. f(x) Objective 3: Apply the Remainder and Factor Theorems 39. The value (-6)%3D39 for a polynomial f(x). What can has a 40. Given a polynomial f(x), the quotient x - 2 f(x) remainder of 12. What is the value of f(2)? E be concluded about the remainder or quotient of x + 6 41. Given f(x) = 2x- 5x + - 7, a. Evaluate f(4). b. Determine the remainder when f(x) is divided by (x-4). 42. Given g(x) = -3x + 2x* + 6x² – x + 4, a. Evaluate g(2). b. Determine the remainder when g(x) is divided by (x – 2). G OL TORG For Exercises 43-46, use the remainder theorem to evaluate the polynomial for the given values of x. (See Example 6) 43.) f(x) = 2x + x - 49x + 79x + 15 44. g(x) = 3x - 22x + 51x – 42x + 8 bivib o t vc. g(1) a. f(-1) b. f(3) c. f(4) 45. h(x) = 5x – 4x - 15x + 12 noizivib gnol o b oti d. f a. g(-1) b. g(2) d. g %3D 46. k(x) = 2x - ² – 14x + 7 a. h(1) 4 b. h c. h(V3) d. h(-1) a. k(2) b. k c. k(V7) d. k(-2) For Exercises 47-54, use the remainder theorem to determine if the given number c is a zero of the polynomial. (See Example 7) с. 2/ib guol saD - 10 3. 7.2 L 13r 10 48. g(r) = 2x + 13r – 10 %3D 10r2 19r 4/3 215
Transcribed Image Text:Chapter 2 Poly 280 3. -4 25.-4 -2 -25 4. 24 1 -4 1-6 28. (6x+25x - 19) ÷ (x + 5) 30. (2x2 + x- 21) (x - 3) (x + 1) 27. (4x + 15x + 1) + (* + 6) 29. (5x-17x-12) (*-4) 31. (4-&r-3-Sr) (+2) 4x-25-58e+ 232+198x-63 21+13x-3x' – 58x – 20x + 24 34. 32. (-5+ 2x + 5x- 2x) | X - 2 x-81 36. x + 3 33. 1-3 2+32 35. よ+2 38. (-5x – 18r + 63x + 128x 60) ÷ 37. (2x- 7- 56x+ 37x + 84) (*- 2. f(x) Objective 3: Apply the Remainder and Factor Theorems 39. The value (-6)%3D39 for a polynomial f(x). What can has a 40. Given a polynomial f(x), the quotient x - 2 f(x) remainder of 12. What is the value of f(2)? E be concluded about the remainder or quotient of x + 6 41. Given f(x) = 2x- 5x + - 7, a. Evaluate f(4). b. Determine the remainder when f(x) is divided by (x-4). 42. Given g(x) = -3x + 2x* + 6x² – x + 4, a. Evaluate g(2). b. Determine the remainder when g(x) is divided by (x – 2). G OL TORG For Exercises 43-46, use the remainder theorem to evaluate the polynomial for the given values of x. (See Example 6) 43.) f(x) = 2x + x - 49x + 79x + 15 44. g(x) = 3x - 22x + 51x – 42x + 8 bivib o t vc. g(1) a. f(-1) b. f(3) c. f(4) 45. h(x) = 5x – 4x - 15x + 12 noizivib gnol o b oti d. f a. g(-1) b. g(2) d. g %3D 46. k(x) = 2x - ² – 14x + 7 a. h(1) 4 b. h c. h(V3) d. h(-1) a. k(2) b. k c. k(V7) d. k(-2) For Exercises 47-54, use the remainder theorem to determine if the given number c is a zero of the polynomial. (See Example 7) с. 2/ib guol saD - 10 3. 7.2 L 13r 10 48. g(r) = 2x + 13r – 10 %3D 10r2 19r 4/3 215
Concept Connections 1. Given the division algorithm, identify the polynomials representing the dividend, divisor, quotient, and remainder. f(x) = d(x) q(x) + r(x) 2x-5x-6x+1 %3D 2. Given 21+x-3 + -- use the division algorithm to check the result. ォ-3 x-3' 3. The remainder theorem indicates that if a polynomial f(x) is divided by x - c, then the remainder is of f(x). 4. Given a polynomial fx), the factor theorem indicates that if f(c) Furthermore, if x- c is a factor of f(x), then f(c) = 0, then x -c is a %3D 5. Answer true or false. If V5 is a zero of a polynomial, then (x- V5) is a factor of the polynomial. 6. Answer true or false. If (r + 3) is a factor of a polynomial, then 3 is a zero of the polynomial. Objective 1: Divide Polynomials Using Long Division For Exercises 7-8, (See Example 1) a. Use long division to divide. b. Identify the dividend, divisor, quotient, and remainder. c. Check the result from part (a) with the division algorithm. 7. (6x + 9x + 5) ÷ (2x – 5) 8. (12x + 10x+ 3) ÷ (3x + 4) For Exercises 9-22, use long division to divide. (See Examples 1-3) 9. (3x - 11x - 10) ÷ (x – 4) 10. (2x – 7x - 65) (x – 5) | 11. (8 + 30x - 27x - 12x + 4xr*) ÷ (x + 2) 12. (-48 - 28r + 20x + 17x + 3x*) ÷ (x + 3) 13. (-20x + 6x - 16) (2x + 4) 14. (-60x + 8x* - 108) (2 – 6) 15. (x+ 4x + 18x- 20x - 10) ÷ (x + 5) 16. (x- 2x+ x'- 8r + 18) ÷ (r - 3) 17. 6x + 3x - 7x + 6x - 5 12x- 4x + 13x² + 2x + 1 18. 17.) 2x + x- 3 3x - x + 4 | x-27 19. x - 3 x' + 64 20. x+ 4, 21. (5x - 2x + 3) (2x - 1) 22. (2r + x + 1) ÷ (3x + 1)
Transcribed Image Text:Concept Connections 1. Given the division algorithm, identify the polynomials representing the dividend, divisor, quotient, and remainder. f(x) = d(x) q(x) + r(x) 2x-5x-6x+1 %3D 2. Given 21+x-3 + -- use the division algorithm to check the result. ォ-3 x-3' 3. The remainder theorem indicates that if a polynomial f(x) is divided by x - c, then the remainder is of f(x). 4. Given a polynomial fx), the factor theorem indicates that if f(c) Furthermore, if x- c is a factor of f(x), then f(c) = 0, then x -c is a %3D 5. Answer true or false. If V5 is a zero of a polynomial, then (x- V5) is a factor of the polynomial. 6. Answer true or false. If (r + 3) is a factor of a polynomial, then 3 is a zero of the polynomial. Objective 1: Divide Polynomials Using Long Division For Exercises 7-8, (See Example 1) a. Use long division to divide. b. Identify the dividend, divisor, quotient, and remainder. c. Check the result from part (a) with the division algorithm. 7. (6x + 9x + 5) ÷ (2x – 5) 8. (12x + 10x+ 3) ÷ (3x + 4) For Exercises 9-22, use long division to divide. (See Examples 1-3) 9. (3x - 11x - 10) ÷ (x – 4) 10. (2x – 7x - 65) (x – 5) | 11. (8 + 30x - 27x - 12x + 4xr*) ÷ (x + 2) 12. (-48 - 28r + 20x + 17x + 3x*) ÷ (x + 3) 13. (-20x + 6x - 16) (2x + 4) 14. (-60x + 8x* - 108) (2 – 6) 15. (x+ 4x + 18x- 20x - 10) ÷ (x + 5) 16. (x- 2x+ x'- 8r + 18) ÷ (r - 3) 17. 6x + 3x - 7x + 6x - 5 12x- 4x + 13x² + 2x + 1 18. 17.) 2x + x- 3 3x - x + 4 | x-27 19. x - 3 x' + 64 20. x+ 4, 21. (5x - 2x + 3) (2x - 1) 22. (2r + x + 1) ÷ (3x + 1)
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