§. Natural va butun sonlar

A)0 B)1 C) a+b+c D) aniqlab bo’lmaydi

42. P() = x²+x+1 shartniqanoatlantiruvchi P(x) ko’phadberilgan. P(3x) = 7 shartiniqanoatlantiradiganbarchax ningqiymatlariyig’indisini toping.

A)–1/9 B) 1/9 C)–2/27 D) 2/27

43. P() = x²+x+1 shartniqanoatlantiruvchi P(x) ko’phadberilgan. P(3x) = 7 shartiniqanoatlantiradiganbarchax ningqiymatlariko’paytmasini toping.

A)– 1/9 B)1/9 C)– 2/27 D) 2/27

44. P(x) = (1+2x–x²)⁴ko’phadning x⁷oldidagikoeffitsiyentinianiqlang.

A)– 6 B)6 C)8 D)– 8

45. Agar 2²⁰⁰⁷ – 2²⁰⁰⁶ – 2²⁰⁰⁵ + 2²⁰⁰⁴ = k∙2²⁰⁰⁴ifodaberilganbo’lsa, k ningqiymatini toping.

A) 1 B)2 C)3 D)4

46. Agar x² + y² = 1 bo’lsa, 3x⁴ + 2y⁴ +5x²y² + y²ningqiymatini toping.

A) 2 B)3 C)9 D)10

47. Agar x² + y² = 1 bo’lsa, 9x⁴ + 6y⁴ +15x²y² +3 y²ningqiymatini toping.

A) 6 B)18C)9 D)10

48. Agar x² + y² = 1 bo’lsa, 6x⁴ + 4y⁴ +10x²y² + 2y²ningqiymatini toping.

A) 4B)6 C)9 D)10

49. Agar x² + y² = 1 bo’lsa, 12x⁴ + 8y⁴ +20x²y² + 4y²ningqiymatini toping.

A) 8 B)12 C)16 D)10

50. (a+1)⁴ + 4 (a+1)³ + 4a(a+ 2) ko’phadnechtaratsionalhadliko’paytuvchilargaajraladi.

A) 3 B)2 C)4 D) ko’paytuvchilargaajralmaydi

51. (a+1)⁴ + 4 (a+1)³ + 4a(a+2)= P(x)∙Q(x) shaklidaberilganifodadan|P(x) – Q(x)|ningqiymatini toping. ( Bunda P(x) va Q(x) ratsionalhadliko’phadlar)

A) 8a+6 B) 2a² + 8a+6 C) 4 D) 8a+4

52. (a+1)⁴ + 4 (a+1)³ + 4a(a+2)= P(x)∙Q(x) shaklidaberilganifodadan P(x) +Q(x)ningqiymatini toping. ( Bunda P(x) va Q(x) ratsionalhadliko’phadlar)

A) 2a² + 8a+4 B) 2a² + 8a+6C) 4 D) 8a+4

53.a³ + b³ +c³ +3a²(b+c)+3b²(a+c)+3c²(a+b)+6abc ifodani ko’paytuvchilarga ajrating.

A) (a+b+c)(a²+b²+c²) B) (a+b+c)(a²+b²+c²-2ab-2bc-2ac) C) (a+b+c)³ D) ko’paytuvchilarga ajralmaydi

54. a³ + b³ +c³ +3a²(b+c)+3b²(a+c)+3c²(a+b)+6abc I fodani a=7, b=2, c=1 bo’lgandagi qiymatini toping.

A) 540 B) 80 C) 1000 D) 900

55. P(x)= (2x²-2x+1)¹⁹⁹⁹ (x³-2x²)²⁰⁰¹ ko’phadni barcha koeffitsientlarini yig’indisini toping.

A) 1 B)-1 C)0 D)2

56. P(x,y)=(5x²-xy-2y)¹² ko’phadni barcha koeffitsientlarini yig’indisini toping.

A)512 B)1024 C)2048 D)4096

57.Agar 3z+4(2─z)=8 bo’lsa, 1+ ifodaning qiymatini toping.

A)2,5 B)3,5 C)1,5 D)4,5

58.(a+b+c)³─a³─b³─c³ifodaquyidagilarningqaysibirigabo’linmaydi?

A) a+bB) a+b+c C) 3 D) barchasigabo’linadi

59.(a+b+c)³─a³─b³─c³ifodanechtako’paytuvchigaajraladi?

A)3 B)5 C)4 D)6

60. Agar a:b:c=2:4:7 bo’lsa, (7a+b)/(c─2) ningqiymatini toping.

A) aniqlabbo’lmaydi B)6 C)8 D)9

61. P(x) ko’phadni (x-1) ga bo’lganda qoldiq 2 chiqadi. Agar (x-2) ga bo’lganda qoldiq 1 bo’lsa, P(x) ko’phadni (x-1)(x-2) ga bo’lganda qoldiqni toping.

A) 3-x B) x+3 C)x-1 D)x-2

62. M=x³-7x²+2 ko’phad

M=(x+1)³+a(x+1)²+b(x+1)+c ko’phad ko’rinishida

keltirilsa, a ning qiymatini toping.

A)17 B)-6 C)-10 D) aniqlab bo’lmaydi

63. M=x³-7x²+2 ko’phad

M=(x+1)³+a(x+1)²+b(x+1)+c ko’phad ko’rinishida

keltirilsa, b ning qiymatini toping.

A)17 B)-6 C)-10 D) aniqlab bo’lmaydi

64. M=x³-7x²+2 ko’phad

M=(x+1)³+a(x+1)²+b(x+1)+c ko’phad ko’rinishida

keltirilsa, c ning qiymatini toping.

A)17 B)-6 C)-10 D) aniqlab bo’lmaydi

65. Soddalashtiring.

66. Soddalashtiring.

67. Soddalashtiring.

68. x, y va z haqiqiy sonlar bo’lsa, (x+y+z)³- (y+z-x)³-(z+x-y)³-(x+y-z)³ ifoda quyidagilardan qaysi biriga teng.

A)36 xyz B)24 xyz C)12 x²y²z² D) 12 xyz

69. x, y va z haqiqiy sonlar bo’lsa, (x-y)(y+z)(z+x)+(y-z)(z+x)(x+y)+(z-x)(x+y)(y+z) ifoda quyidagilardan qaysi biriga teng.

A)(x-y)(y-z)(z-x) B) -(x-y)(y-z)(z-x) C) (x+y)(y+z)(z-x) D) (x+y)(y+z)(z+x)

70.x, y va z haqiqiy sonlar bo’lsa, P(x,y,z)=x³+y³+z³-3xyz ko’phad uchun quyidagilardan qaysi biri qanoatlantiradi.

A) P(x,y,z)=P(x+y,y+z,z+x) B) P(x,y,z)=P(x-y,y-z,z+x) C) P(x,y,z)= P(x+y,y+z,z+x)

D) P(x,y,z)=P(x+2y,y+2z,z+2x)

71.x, y va z haqiqiy sonlar bo’lsa, P(x,y,z)=x³+y³+z³-3xyz ko’phad uchun quyidagilardan qaysi biri qanoatlantiradi.

A) P(x,y,z)= P(-x+y+z,x-y+z,x+y-z) B) P(x,y,z)=P(-x+y+z,x-y+z,x+y-z) C) P(x,y,z)= P(-x+y+z,x-y+z,x+y-z) D) P(x,y,z)=P(-2x+y+z,x-2y+z,x+y-2z)

72. a,b,c nol bo’lmagan haqiqiy sonlar uchun a+ shart qanoatlantirsa, ning qiymatini hisoblang.