CBSE Class 9 Polynomials Sure Shot Questions

Mathematics
Download PDF

Read and download free pdf of CBSE Class 9 Polynomials Sure Shot Questions. Students and teachers of Class 9 Mathematics can get free advanced study material, revision notes, sure shot questions and answers for Class 9 Mathematics prepared as per the latest syllabus and examination guidelines in your school. Class 9 students should download this study material which will give them more knowledge for all chapters in Mathematics and all important topics which are scoring and can get you more marks. Students should also download free pdf of Chapter wise Notes for Class 9 Mathematics prepared by school teachers as per the latest NCERT, CBSE, KVS books and syllabus issued this year and also download free worksheets and question papers available here to get higher scores in school exams and tests, also click here for more Study Material for Class 9 Mathematics

Study Material for Class 9 Mathematics Chapter 2 Polynomials

Class 9 Mathematics students should refer to the following Pdf for Chapter 2 Polynomials in Class 9. These notes and test paper with questions and answers for Class 9 Mathematics will be very useful for exams and help you to score good marks

Class 9 Mathematics Chapter 2 Polynomials

 

CBSE Class 9 Polynomials Sure Shot Questions. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

1. Factorize the following: 9x2 + 6x + 1 – 25y2.

2. Factorize the following: a2 + b2 + 2ab + 2bc + 2ca

3. Show that p(x) = x3 – 3x2 + 2x – 6 has only one real zero.

4. Find the value of a if x + 6 is a factor of x3 + 3x2 + 4x + a.

5. If polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a leaves the same remainder when each is divided byx – 4, find the value of a..

6. The polynomial f(x)= x4 – 2x3 +3x2 – ax + b when divided by (x – 1) and (x + 1) leaves the remainders 5 and 19 respective ly. Find the values of a and b. Hence, find the remainder when

f(x) is divided by (x – 2).

7. If the polynomials 2x3 +ax2 + 3x – 5 and x3 + x2 – 2x + a leave the same remainder when divided by (x – 2), find the value of a. Also, find the remainder in each case.

8. If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.

9. The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.

10. If both x – 2 and x – 1/ 2 are factors of px2 + 5x + r, show that p = r.

11. Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2.

12. Simplify (2x – 5y)3 – (2x + 5y)3.

13. Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (– z + x – 2y).

14. If a, b, c are all non-zero and a + b + c = 0, prove that 

useful-resources-polynomials-cbse-class-9-polynomials

15. If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 –3abc = – 25.

16. Without actual division, prove that 2x4 – 6x3 +3x2 +3x – 2 is exactly divisible by x2 – 3x + 2.

17. Without actual division, prove that x3 – 3x2 – 13x + 15 is exactly divisible by x2 + 2x – 3.

18. Find the values of a and b so that the polynomial x3 – 10x2 +ax + b is exactly divisible by (x – 1) as well as (x – 2).

19. Find the integral zeroes of the polynomial 2x3 + 5x2 – 5x – 2.

20. If (x – 3) and x -1/3 are both factors of ax2 + 5x + b, then show that a = b.
 
21. Find the values of a and b so that the polynomial x4 + ax3 – 7x2 +8x + b is exactly divisible by (x + 2) as well as (x + 3).
 
22. If x3 + ax2 + bx + 6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), find the values of a and b.
 
23. Find the value of x3 + y3 + 15xy – 125 if x + y = 5.
 
24. Without actually calculating, find the value of (25)3 – (75)3 + (50)3.
 
25. Factorise each of the following cubic expressions:
 
(i) 8x3 – y3 – 12x2y + 6xy2
 
(ii) 27q3 – 125p3 – 135q2p + 225qp2
 
(iii) 8x3 + 729 + 108x2 + 486x
 
(iv) 27x3 - 1/216-9/2x2 + 1/4x
 
26. Factorise:
 
(i) x3 + 216y3 + 8z3 – 36xyz
 
(ii) a3 – 64b3 – 27c3 – 36abc
 
28. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
 
29. Find a zero of the polynomial p(x) = 2x + 1.
 
30. Verify whether 2 and 0 are zeroes of the polynomial x2 – 2x.
 
31. Find the zero of the polynomial in each of the following cases:
 
(i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5
 
(iv) p(x) = 3x – 2 (v) p(x) = 3x (vi) p(x) = ax, a ≠ 0
 
32. Find the value of each of the following polynomials at the indicated value of variables:
 
(i) p(x) = 5x2 – 3x + 7 at x = 1.
 
(ii) q(y) = 3y3 – 4y + 11 at y = 2.
 
(iii) p(t) = 4t4 + 5t3 – t2 + 6 at t = a.
 
33. Divide p(x) by g(x), where p(x) = x + 3x2 – 1 and g(x) = 1 + x.
 
34. Divide the polynomial 3x4 – 4x3 – 3x –1 by x – 1.
 
35. Find the remainder obtained on dividing p(x) = x3 + 1 by x + 1.
 
36. Find the remainder when x4 + x3 – 2x2 + x + 1 is divided by x – 1.
 
37. Check whether the polynomial q(t) = 4t3 + 4t2 – t – 1 is a multiple of 2t + 1.
 
38. Check whether p(x) is a multiple of g(x) or not, where p(x) = x3 – x + 1, g(x) = 2 – 3x.
 
39. Check whether g(x) is a factor of p(x) or not, where p(x) = 8x3 – 6x2 – 4x + 3, g(x) = x/3-1/4
 
40. Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
 
41. Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6 and of 2x + 4.
 
42. Find the value of k, if x – 1 is a factor of 4x3 + 3x2 – 4x + k.
 
43. Find the value of a, if x – a is a factor of x3– ax2 + 2x + a – 1.
 
44. Factorise 6x2 + 17x + 5
 
45. Factorise y2 – 5y + 6
 
46. Factorise x3 – 23x2 + 142x – 120.
 
47. Factorise :
(i) x3– 2x2 – x + 2 (ii) x3 – 3x2 – 9x – 5
 
(iii) x3+ 13x2 + 32x + 20 (iv) 2y3 + y2 – 2y – 1
 
48. Factorise : 4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
 
49. Expand (4a – 2b – 3c)2.
 
50. Factorise 4x2 + y2 + z2 – 4xy – 2yz + 4xz.
 
51. If x + 1 is a factor of ax3 + x2 – 2x + 4a – 9, find the value of a.
 
52. By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial : x4 + 1; x –1
 
53. Find the zeroes of the polynomial : p(x) = (x – 2)2 – (x + 2)2
 
54. Factorise :
(i) x2 + 9x + 18 (ii) 6x2 + 7x – 3
 
(iii) 2x2 – 7x – 15 (iv) 84 – 2r – 2r2
 
55. Factorise :
 
(i) 2x3 – 3x2 – 17x + 30 (ii) x3 – 6x2 + 11x – 6
 
(iii) x3 + x2 – 4x – 4 (iv) 3x3 – x2 – 3x + 1
 
56. Using suitable identity, evaluate the following:
 
(i) 1033 (ii) 101 × 102 (iii) 9992
 
57. Factorise the following:
 
(i) 4x2 + 20x + 25
 
(ii) 9y2 – 66yz + 121z2
 
(iii) (2x+1/3)2 - (x-1/2)2
 
58. Factorise the following :
 
(i) 9x2 – 12x + 3 (ii) 9x2 – 12x + 4
 
59. If a + b + c = 9 and ab + bc + ca = 26, find a2 + b2 + c2.
 
60. Expand the following :
 
(i) (4a – b + 2c)2
 
(ii) (3a – 5b – c)2
 
(iii) (– x + 2y – 3z)2
 
61. Find the value of
 
(i) x3 + y3 – 12xy + 64, when x + y = – 4
 
(ii) x3 – 8y3 – 36xy – 216, when x = 2y + 6
 
62. Factorise the following :
 
(i) 9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
 
(ii) 25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
 
(iii) 16x2 + 4y2 + 9z2 – 16xy – 12yz + 24 xz
CBSE Class 9 Polynomials Sure Shot Questions
 
66. Without finding the cubes, factorise (x – 2y)3 + (2y – 3z)3 + (3z – x)3
 
67. Give possible expressions for the length and breadth of the rectangle whose area is given by 4a2 + 4a –3.
 
68. Factorise: (i) 1+ 64x3 (ii) a3 + 2 2b3
 
69. Evaluate each of the following using suitable identities:
(i) (104)3         (ii) (999)3
 
70. Factorise : 8x3 + 27y3 + 36x2y + 54xy2
 
71. Factorise : 8x3 + y3 + 27z3 – 18xyz
 
72. Verify : (i) x3 + y3 = (x + y) (x2 – xy + y2) (ii) x3 – y3 = (x – y) (x2 + xy + y2)
 
73. Factorise each of the following:
 
(i) 27y3 + 125z3 (ii) 64m3 – 343n3
 
74. Factorise : 27x3 + y3 + z3 – 9xyz
 
75. Without actually calculating the cubes, find the value of each of the following:
 
(i) (–12)3 + (7)3 + (5)3
 
(ii) (28)3 + (–15)3 + (–13)3
 
76. Find the following product :(2x – y + 3z) (4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) 77. Factorise :
 
(i) a3 – 8b3 – 64c3 – 24abc (ii) 2 2 a3 + 8b3 – 27c3 + 18 2 abc.
 
78. Give possible expressions for the length and breadth of rectangles, in which its areas is given by 35y2 + 13y –12
 
79. Without actually calculating the cubes, find the value of :
 
(i) (1/2)3 +(1/3)3 - (5/6)
 
(ii) (0.2)3 - (0.3)3 + (0.1)3
 
80. By Remainder Theorem find the remainder, when p(x) is divided by g(x), where
(i) p(x) = x3 – 2x2 – 4x – 1, g(x) = x + 1
 
(ii) p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
 
(iii) p(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1
 
(iv) p(x) = x3 – 6x2 + 2x – 4, g(x) = 1 3/2x
 
81. Check whether p(x) is a multiple of g(x) or not :
 
(i) p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
 
(ii) p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
 
82. Show that p – 1 is a factor of p10 – 1 and also of p11 – 1.
 
83. For what value of m is x3 – 2mx2+ 16 divisible by x + 2 ?
 
84. If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
 
85. Find the value of m so that 2x – 1 be a factor of 8x4 + 4x3 – 16x2 + 10x + m.
 
86. Show that :
 
(i) x + 3 is a factor of 69 + 11x – x2 + x3 .
 
(ii) 2x – 3 is a factor of x + 2x3 – 9x2 + 12 .
 
87. If x + y = 12 and xy = 27, find the value of x3 + y3
 
88. Without actually calculating the cubes, find the value of 483 – 303 – 183.
 
89. Without finding the cubes, factorise (2x – 5y)3 + (5y – 3z)3 + (3z – 2x)3.
 
90. Without finding the cubes, factorise (x – y)3 + (y – z)3 + (z – x)3.
 

Please click the link below to download CBSE Class 9 Polynomials Sure Shot Questions.

Chapter 01 Number Systems
CBSE Class 9 Number Systems Sure Shot Questions
Chapter 02 Polynomials
CBSE Class 9 Polynomials Sure Shot Questions
Chapter 03 Coordinate Geometry
CBSE Class 9 Coordinate Geometry Sure Shot Questions
Chapter 04 Linear Equations In Two Variables
CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions
Chapter 05 Introduction to Euclids Geometry
CBSE Class 9 Introduction to Euclids Geometry Sure Shot Questions
Chapter 06 Lines and Angles
CBSE Class 9 Lines and Angles Sure Shot Questions
Chapter 07 Triangles
CBSE Class 9 Triangles Sure Shot Questions
Chapter 08 Quadrilaterals
CBSE Class 9 Quadrilaterals Sure Shot Questions
Chapter 09 Areas of Parallelograms and Triangles
CBSE Class 9 Areas of Parallelogram and Triangle Sure Shot Questions
Chapter 10 Circles
CBSE Class 9 Circles Sure Shot Questions
Chapter 11 Constructions
CBSE Class 9 Constructions Sure Shot Questions
Chapter 12 Herons Formula
CBSE Class 9 Herons Formula Sure Shot Questions
Chapter 13 Surface Areas and Volumes
CBSE Class 9 Surface Areas and Volumes Sure Shot Questions
Chapter 14 Statistics
CBSE Class 9 Statistics Sure Shot Questions
Chapter 15 Probability
CBSE Class 9 Probability Sure Shot Questions
Tags
CBSE NCERT Study Material
Class 9 Polynomials Exam Notes
Class 9 Polynomials mind maps
Class 9 Polynomials sure shot questions
Class 9 Polynomials
Class 9 Polynomials Important Questions
Class 9 Polynomials Chapter Summary

CBSE Class 9 Mathematics Chapter 2 Polynomials Study Material

We hope students liked the above Study Material for Chapter 2 Polynomials designed as per the latest syllabus for Class 9 Mathematics released by CBSE. Students of Class 9 should download the Study Material in Pdf format, read the notes and related questions and solutions given in above Class 9 Mathematics Study Material on daily basis. All latest Study Material have been developed for Mathematics by referring to the most important and regularly asked topics which the students should learn and practice to get better score in school tests and examinations. Expert teachers of studiestoday have referred to NCERT book for Class 9 Mathematics to develop the Mathematics Class 9 Study Material. After solving the questions given in the Study Material which have been developed as per latest course books also refer to the NCERT solutions for Class 9 Mathematics designed by our teachers. Also download Class 9 Mathematics Sample Papers given on studiestoday. After solving these you should also refer to Class 9 Mathematics MCQ Test for the same chapter.

 

How to download CBSE Class 9 Mathematics Chapter 2 Polynomials study material

You can download free study material for Class 9 Mathematics Chapter 2 Polynomials for latest academic session from StudiesToday.com

Is the study material for Chapter 2 Polynomials Class 9 Mathematics for the latest CBSE academic session

Yes, the study material given here for Class 9 Mathematics Chapter 2 Polynomials is for current CBSE session

Is there any charge for Class 9 Mathematics Chapter 2 Polynomials concepts and study material

All study maetrial for CBSE Class 9 Mathematics Chapter 2 Polynomials is free