Academy of Chinese Culture Polynomial and Rational Functions Problems

Polynomia and Rational Functions

356
Chapter 5 Polynomials and Rational Functions
29.
2x + x-3
x-1
3x) – 2x + 1
30.
* – 5
31.
x + 2x + 1
x + 4
32. ** – 3x² + 1
X – 4
33.
XS – 2x + x – 3x? – x + 1
x – 2
34.
2×5 – 3×4 + x – x2 + 2x + 1
x + 2
35.
x? + x + 1
x-1
36.
x2 + x +1
x+1
37.
x-1
x + 1
**+1
38.
X-1
39.
x-1
X-1
40.
x-1
x + 1
Use synthetic division to identify the quotient and remainder when P(x) is
divided by f(x).
41. P(x) = x2 + 3x – 4, f(x) = x – 5
42. P(x) = 3×2 + 5x – 2,f(x) = x – 1
43. P(x) = x – 2×2 + 5x + 4, f(x) = x + 3
44. P(x) = x3 – 5x + 2x – 3, f(x) = x + 4
45. P(x) = 5x – 2×2 + 4, f(x) = x – 3
46
P = 773 – Ay Lify)
2
44. P(x) x – 5x + 2x – 3, f(x) = x + 4
45. P(x) = 5×3 – 2×2 + 4, f(x) = x – 3
46. P(x) = 7×3 – 4×2 + 1, f(x) = x – 2
Use a table like the one in Example 13 to work the following problems.
* -Ź
47. Divide 2×3 – 3×2 + 5x – 6 by x – 3, x – x + 1, and x + 2.
48. Divide 3×3 + 5×2 + 5x – 6 by x – 3, x – 5,x + 1, and x + 2.
1
2
49. Find the remainders when 2×3 – 9×2 + 3 is divided by x – 3,2 – žıx+1,
and x + 2.
50. Find the remainders when 4x – 3×2 – 2 is divided by x – 2,8 – 3,x+
and x + 3.
51. Factor x’ + 6×2 + 11x + 6 completely if one of its factors is x + 3.
52. Factor x + 10×2 + 29x + 20 completely if one of its factors is x + 4.
53. Factor x’ + 5×2 – 2x – 24 completely if one of its factors is x + 3.
54. Factor x3 + 3×2 – 10x – 24 completely if one of its factors is x + 2.
55. Find P(-2) if P(x) = x2 – 5x + 6. Compare it with the remainder in Problem
21.
56. Find P(3) if P(x) = x2 + 4x – 8. Compare it with the remainder in Problem 13.