Please complete problems: 1, 2, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 39, 41, 43

Please show all work and solve on paper if possible

Verbal 1. If division of a polynomial by a binomial results in a remainder of zero, what can be conclude? 2. If a polynomial of degree n is divided by a binomial of degree 1, what is the degree of the quotient? Algebraic For the following exercises, use long division to divide. Specify the quotient and the remainder. 3. (x2 + 5x - 1) + (x - 1) 4. (2x2 - 9x - 5) + (x -5) 5. (3x2 + 23x + 14) + (x +7) 6. (4x2 - 10x + 6) + (4x + 2) 7. (6x2 - 25x - 25) + (6x + 5) 8. (-x2 - 1) + (x + 1) 9. (2x2 - 3x + 2) + (x+ 2) 10. (x3 - 126) + (x - 5) 11. (3x2 - 5x + 4) + (3x + 1) 12. (x3 - 3x2 + 5x - 6) + (x - 2) 13. (2x3 + 3x2 - 4x + 15) + (x + 3) For the following exercises, use synthetic division to find the quotient. 14. (3x3 - 2x2 + x - 4) + (x+3) 15. (2x3 - 6x2 - 7x+ 6) + (x -4) 16. (6x3 - 10x2 - 7x - 15) + (x + 1) 17. (4x3 - 12x2 - 5x - 1) + (2x + 1) 18. (9x3 - 9x2 + 18x + 5) + (3x - 1) 19. (3x3 - 2x2 + x - 4) + (x + 3) 20. (-6x3 + x2 - 4) + (2x - 3) 21. (2x3 + 7x2 - 13x - 3) + (2x - 3) 22. (3x3 - 5x2 + 2x + 3) + (x +2) 23. (4x3 - 5x2 + 13) + (x + 4) 24. (x3 - 3x + 2) + (x + 2) 25. (x3 - 21x2 + 147x - 343) + (x - 7) 26. (x3 - 15x2 + 75x - 125) + (x -5) 27. (9x3 - x + 2) + (3x - 1) 28. (6x3 - x2 + 5x + 2) + (3x + 1) 29. (x4 + x3 - 3x2 - 2x + 1) + (x + 1) 30. (x4 - 3x2 + 1) + (x - 1) 31. (x4 + 2x3 - 3x2+ 2x + 6) + (x+3) 32. (x4 - 10x3 + 37x2 - 60x + 36) + (x - 2) 33. (x4 - 8x3 + 24x2 - 32x + 16) + (x - 2) 34. (x4 + 5x3 - 3x2 - 13x + 10) + (x +5) 35. (x4 - 12x3 + 54x2 - 108x + 81) + (x - 3) 36. (4x4 - 2x3 - 4x + 2) + (2x - 1) 37. (4x4 + 2x3 - 4x2 + 2x + 2) + (2x + 1) For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. 38. x - 2, 4x3 - 3x2 - 8x + 4 39. x - 2, 3x4 - 6x3 - 5x + 10 40. x+ 3, -4x3 + 5x2 + 8 41. x - 2, 4x4 - 15x2 - 4 42. x - , 2x4 - x3 + 2x - 1 43. x+ 3, 3x4 + x3 - 3x + 1