Need help on Question #13, #19, # 21 and #43. Concept Connections1. 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 + 1-8= 21 + x- 3+use the division algorithm to check the result.2. Given3'3. The remainder theorem indicates that if a polynomial f(x) is divided by x- c, then the remainder is4. Given a polynomial fx), the factor theorem indicates that if f(c) = 0, then x- c is aFurthermore, if x- c is a factor of fx), then f(c) =of f(x).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 (x + 3) is a factor of a polynomial, then 3 is a zero of the polynomial.Objective 1: Divide Polynomials Using Long DivisionFor 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. (121 + 10x + 3) ÷ (3x + 4)For Exercises 9-22, use long division to divide. (See Examples 1-3)9. (3x - 11 - 10) (x - 4)10. (2x - 7x – 65) ÷ (x – 5)11. (8 + 30x - 27x - 12x + 4x*) ÷ (x + 2)12. (-48 28x + 20x + 17x + 3x*) ÷ (x + 3)13. (-20x + 6x - 16) (2x + 4)14. (-60x + 8x - 108) (2x - 6)15. (r + 4x + 18x - 20x - 10) (x² + 5)16. (х2x + x- 8x + 18) (x- 3)6x + 3x-7x+ 6x - 5(17.12 4x+ 13x² + 2x + 118.2x2 + x- 33x - x + 4x' - 2719.x - 3x'+ 6420.x+ 4,21. (5x' - 2x +3) (2x- 1)22. (2x + x* + 1) + (3x + 1) Chapter 2 Poly280-4-224-2525.-4 1-7101-630. (2r +x-21) (x-3)32. (-5 +2x + 5x - 2x) ÷ (x + 1)2x+ 13x-3x – 58x² – 20x + 2434.28. (6x + 25x 19) + (x + 5)27. (4x + 15x +1)+ a + 6)29. (Sx-17-12) (x-4)31. (4-&r-3-Sx)+(x+ 2)4-25-58+232+198x-63x- 233.-3- 8135.x+22+3236.x + 3- 60) (x-)37. (2x- 7x- 56x + 37x + 84)38. (-5x- 18x + 63x + 128x -Objective 3: Apply the Remainder and Factor Theoremsf(x)has a39. The value f-6) = 39 for a polynomial f(x). What can40. Given a polynomial f(x), the quotientX - 2f(x)be concluded about the remainder or quotient ofremainder of 12. What is the value of f(2)?x + 641. Given f(x) = 2x - 5x + x² - 7,a. Evaluate f(4).42. Given g(x) = -3x + 2x* + 6x² – x + 4,a. Evaluate g(2).b. Determine the remainder when f(x) is divided by(x-4).b. Determine the remainder when g(x) is divided by(х - 2).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 + 1544. g(x) = 3x – 22x + 51x – 42x + 8a. f(-1)b. f(3)c. f(4)45. h(x) = 5x – 4x – 15x + 12d.vibgnol oald. ga. g(-1)b. g(2)c. g(1)46. k(x) = 2x-x² - 14x + 7a. h(1)b. hc. h(V3)с.d. h(-1)a. k(2)b. kd. 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 7c. k(V7)7.2 131048. g(r) = 2x + 13r - 10219r + 14

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Description: Need help on Question #13, #19, # 21 and #43. Concept Connections1. 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 + 1-8= 21 + x- 3+use the division a