Maths 1 week 4 important questions

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1. Q4Let p(x)=3 x2 - x + 1 and q(x)=3 x5 + 3 x2 + 3. Find the degree of q(p(x)). Select all the
2. Q5Let p(x)=2 x4 + x2 + 2 and q(x)=2 x4 - 3 x + 1. Find the degree of p(x)-q(x).
3. Q6Let p(x)=x6 + x + 1 and q(x)=- 2 x3 - 3 x2 + 3. Find the degree of (p(x))2+q(x).
4. Q7Let p(x)=2 x3 + x2 + 1 and q(x)=- 2 x3 + 3 x. Find the degree of p(x)+q(x).
5. Q8Let p(x)=3 x2 - 3 x + 3 and q(x)=- x6 - 3 x2 + 4. Find the degree of p(x), ,q(x).
6. Q9Let p(x)=- x5 - 2 x + 2 and q(x)=2 x3 - x2 + 2. Find the degree of (p(x))2, ,q(x).
7. Q10Let p(x)=x4 - 3 x + 4 and q(x)=3 x2 + 3. Find the degree of p(q(x)).
8. Q11Let p(x)=x5 + 2 x + 1 and q(x)=3 - x2. Select all the true statements.
9. Q12Let p(x)=x4 + 2 x + 1 and q(x)=3 - x3. Select all the true statements.
10. Q13Let p(x)=x3 + 2 x + 1 and q(x)=3 - x6. Select all the true statements.
11. Q14Let p(x)=x7 + 2 x + 1 and q(x)=3 - x2. Select all the true statements.
12. Q15Which of the following is a polynomial in x?
13. Q16Exactly one of these expressions is a polynomial. Which one?
14. Q17Choose the expression that is a polynomial in x.
15. Q18Which one of the four functions below is a polynomial?
16. Q19Find the degree of p(x)=2(x-1)2(x+3)(x-4)3.
17. Q20How many distinct real roots does p(x)=-x(x-2)2(x+2) have? Select all the true statements
18. Q21How many turning points does the graph of p(x)=3(x+1)4(x-3) have?
19. Q22For p(x)=(x+4)5(x-4)3(x+12)4, what is the sign of p(5)?
20. Q23For p(x)=-2(x-1)(x-5)2(x+2)3, what happens to p(x) as x+?
21. Q24At how many of its roots does the graph of p(x)=(x-2)4(x+1)7(x-5)2 cross the x-axis (chang
22. Q25At how many of its roots does the graph of p(x)=-3x2(x-3)3 touch the x-axis without crossi
23. Q26Find the degree of p(x)=2(x+2)(x-1)(x-6)2.
24. Q27How many turning points does the graph of p(x)=-(x-1)3(x-2)3(x+3)2 have?
25. Q28For p(x)=x3(x-4)(x+1)2, what is the sign of p(-6)?
26. Q29How many distinct real roots does p(x)=-2(x+3)2(x-2) have?
27. Q30At how many of its roots does the graph of p(x)=4(x-1)5(x+2)2 cross the x-axis (change sig
28. Q31Let p(x)=2(x-1)2(x+3)3(x-5). Select all the true statements.
29. Q32Let p(x)=-x4(x-2)(x+2)5. Select all the true statements.
30. Q33Let p(x)=3(x+1)3(x-4)2(x-7). Select all the true statements.
31. Q34Find the remainder when x4 + 2 x3 - 3 x + 1 is divided by x-2.
32. Q35Find the remainder when x4 + x3 - 2 x + 5 is divided by x-(-1).
33. Q36Find the remainder when x4 + 3 x3 - 6 x + 5 is divided by x-3.
34. Q37Find the remainder when x4 + 2 x3 - 4 x + 5 is divided by x-(-2).
35. Q38The polynomial p(x)=x3+kx2-5x-3 is divisible by x-1. Find k.
36. Q39The polynomial p(x)=x3+kx2-5x-5 is divisible by x-(-1). Find k.
37. Q40The polynomial p(x)=2 x4 + 3 x is divided by q(x)=x2 + x, giving p=q, ,s+r with r< q. Find
38. Q41The polynomial p(x)=x4 + 3 x3 + 3 x2 - 2 x - 6 is divided by q(x)=x2 - 1, giving p=q, ,s+r
39. Q42The polynomial p(x)=x4 + 4 x3 + 4 x2 + 4 x + 2 is divided by q(x)=x2 + x, giving p=q, ,s+r
40. Q43The polynomial p(x)=x4 + x - 1 is divided by q(x)=x2 - 1, giving p=q, ,s+r with r< q. Find
41. Q44The polynomial p(x)=2 x4 + x3 + x2 + 3 x - 1 is divided by q(x)=x2 + x, giving p=q, ,s+r w
42. Q45The polynomial p(x)=2 x4 - x2 + 3 x is divided by q(x)=x2 - 1, giving p=q, ,s+r with r< q.
43. Q46Which of the following is a factor of p(x)=x3 + 5 x2 + 2 x - 8?
44. Q47Which of the following is a factor of p(x)=x3 - x2 - 14 x + 24?
45. Q48The cubic equation x3 - 6 x2 + 11 x - 6=0 has three real roots. Find the sum of the roots.
46. Q49The cubic equation x3 - 5 x2 + 2 x + 8=0 has three real roots. Find the product of the roo
47. Q50The cubic equation x3 - 19 x + 30=0 has three real roots. Find the sum of the squares of t
48. Q51The cubic equation x3 - 4 x2 - 15 x + 18=0 has three real roots. Find the sum of the produ
49. Q52The cubic equation x3 - 2 x2 - 13 x - 10=0 has three real roots. Find the sum of the roots
50. Q53The cubic equation x3 - 11 x2 + 38 x - 40=0 has three real roots. Find the sum of the squa
51. Q54The cubic equation x3 + 2 x2 - 7 x + 4=0 has three real roots. Find the product of the roo
52. Q55The cubic equation x3 - 2 x2 - 9 x + 18=0 has three real roots. Find the sum of the produc
53. Q56The cubic equation x3 - 6 x2 - x + 30=0 has three real roots. Find the sum of the squares
54. Q57The cubic equation x3 + 7 x2 + 14 x + 8=0 has three real roots. Find the sum of the roots.
55. Q58The cubic equation x3 - 5 x2 + 2 x + 8=0 has three real roots. Find the sum of the product
56. Q59The cubic equation x3 - 31 x + 30=0 has three real roots. Find the product of the roots.
57. Q60A cubic polynomial has roots 1, 2 and 3 and passes through (-1,24). Find its value at x=4.
58. Q61A cubic polynomial has roots -1, 1 and 2 and passes through (5,-72). Find its value at x=3
59. Q62A cubic polynomial has roots 0, 2 and 5 and passes through (-1,-18). Find its value at x=1
60. Q63A cubic polynomial has roots -2, 1 and 4 and passes through (-1,-10). Find its value at x=
61. Q64A quadratic polynomial takes the values 1, 4, 11 at x=0, 1, 2. Find its value at x=3.
62. Q65A quadratic polynomial takes the values 6, 2, 12 at x=-1, 0, 2. Find its value at x=1.
63. Q66A quadratic polynomial takes the values 3, 3, 7 at x=1, 2, 3. Find its value at x=4.
64. Q67A cubic polynomial satisfies p(1)=p(2)=p(3)=0 and p(0)=-12. Find p(4).
65. Q68A cubic polynomial satisfies p(-1)=p(1)=p(2)=0 and p(0)=6. Find p(-2). Select all the true
66. Q69A cubic polynomial satisfies p(0)=p(1)=p(4)=0 and p(-3)=-84. Find p(5).
67. Q70A student's score in mock test number n (n=1,2,,12) follows S(n)=50+n(n-5)(n-10)/6. For wh
68. Q71A student's score in mock test number n (n=1,2,,12) follows S(n)=70-n(n-5)(n-10)/6. What i
69. Q72A student's score in mock test number n (n=1,2,,12) follows S(n)=40+(n-1)(n-6)(n-11)/6. In
70. Q73A student's score in mock test number n (n=1,2,,12) follows S(n)=45+n(n-5)(n-10)/6. What i
71. Q74A student's score in mock test number n (n=1,2,,12) follows S(n)=80-(n-2)(n-7)(n-12)/6. Fo
72. Q75A student's score in mock test number n (n=1,2,,12) follows S(n)=75-(n-1)(n-6)(n-11)/6. In
73. Q76A student's score in mock test number n (n=1,2,,12) follows S(n)=55+n(n-5)(n-10)/6. For wh
74. Q77The figure shows the graph of a polynomial with its roots on the x-axis marked as dots. Wh
75. Q78Look at the graph of the polynomial in the figure, whose x-intercepts are marked. Find the
76. Q79A polynomial is drawn in the figure and its zeros are shown as dots. What is the minimum p
77. Q80From the graph in the figure (zeros marked), find the smallest degree that the polynomial
78. Q81The dots in the figure are the zeros of a polynomial whose graph is shown. What is the low
79. Q82Using the crossings and touches shown in the figure, find the least possible degree of the
80. Q83The figure shows the graph of a polynomial p(x) with its x-intercepts marked. Select all t
81. Q84Study the graph of the polynomial p(x) in the figure and select every statement that is tr
82. Q85A polynomial p(x) is drawn in the figure with its zeros marked. Which of the following sta
83. Q86Using the graph of p(x) in the figure, choose all the statements that hold.
84. Q87The graph in the figure belongs to a polynomial p(x). Mark every true statement about it.
85. Q88Read the graph of p(x) in the figure carefully. Which statements are true?
86. Q89The figure shows the graphs of two polynomials y=p(x) and y=q(x). How many real solutions
87. Q90Two polynomial curves y=p(x) and y=q(x) are drawn in the figure. At how many points do the
88. Q91In the figure, p is drawn as a continuous line and q as a dashed line. Find the number of
89. Q92The graphs of p(x) and q(x) appear in the figure. Count the real solutions of p(x)-q(x)=0.
90. Q93The figure shows the graph of a polynomial and the horizontal line y=3. How many real solu
91. Q94A polynomial curve and the line y=2 are drawn in the figure. At how many points do they me
92. Q95Using the figure, find the number of real values of x for which p(x)=-2.
93. Q96The dotted line in the figure is y=4. How many points does it have in common with the grap
94. Q97The figure shows a cubic polynomial (its graph meets the x-axis at the marked points and o
95. Q98The figure shows a cubic polynomial (its graph meets the x-axis at the marked points and o
96. Q99The figure shows a cubic polynomial (its graph meets the x-axis at the marked points and o
97. Q100The figure shows a cubic polynomial (its graph meets the x-axis at the marked points and o