CBSE Class 9 Mathematics Polynomials Worksheet Set 03

Question. Which of the following is a constant polynomial?
(a) x + 1/x − 3
(b) 1/x + 3
(c) √x + 2
(d) – 4
Answer : D

Question. Which of the following polynomials has – 5 as its zero?
(a) (x – 5)
(b) x² – 25
(c) x² – 5x
(d) x² + 5
Answer : B

Question. Using algebraic identity, find the value of 209 × 191.
(a) 39851
(b) 39919
(c) 39961
(d) 38951
Answer : B

Question. If a + b + c = 13 and ab + bc + ca = 84, then find the value of a² + b² + c².
(a) 1
(b) 2
(c) 3
(d) 4
Answer : A

Question. If p(x) = x¹⁶⁰ + 2x¹⁴¹ + k and p(–1) = 0, then the value of k is
(a) 1
(b) – 3
(c) 2
(d) – 2
Answer : A

Question. Factors of polynomial 12x² + 7x + 1 are
(a) (3x – 1)(4x + 1)
(b) (3x – 1)(4x – 1)
(c) (4x – 1)(3x– 1)
(d) (4x + 1)(3x + 1)
Answer : D

Question. If p(x) = x + 3, then p(x) + p(– x) is equal to
(a) 3
(b) 2x
(c) 0
(d) 6
Answer : D

Question. If the volume of a cuboid is x³ + x² – 9x – 9, then its possible dimensions are
(a) x + 1, x², x + 3
(b) x + 1, x – 3, x + 3
(c) 3, x², 9x
(d) 3, 3, 3
Answer : B

Question. The degree of the polynomial (y³ – 3)(y² + 8) is
(a) 2
(b) 3
(c) 0
(d) 5
Answer : D

Question. One of the zeroes of the polynomial 2x² + 7x – 4 is
(a) 2
(b) 1/2
(c) −(1/2)
(d) – 2
Answer : B

Question. If a/b + b/a = 1, then a³ + b³ equals
(a) 1
(b) – 1
(c) 1/2
(d) 0
Answer : D

Question. If p(y) = y² – y + 1, then find the value of p(0) – p(1).
(a) 1
(b) 3
(c) 0
(d) 2
Answer : C

Question. If p(x) = x² + kx + 6, then for what value of k, p(3) = 0 ?
(a) 2
(b) –5
(c) 3
(d) – 1
Answer : B

Question. The value of (9)³ + (– 3)³ is
(a) – 81
(b) 54
(c) 164
(d) 702
Answer : D

Question. If a³ + b³ + c³ = 3abc, then a²/bc + b²/ca + c²/ab =
(a) 0
(b) 1
(c) – 1
(d) 3
Answer : D

Question. The coefficient of the highest power of x in the polynomial 3x³ – 4x⁴ + 5x² – 2x⁵ + 3 is
(a) 2
(b) – 4
(c) 3
(d) –2
Answer : D

Question. Factorise: x² + (a + b + c)x + ab + bc
(a) (x + a)(x + b + c)
(b) (x + a)(x + a + c)
(c) (x + b)(x + a + c)
(d) (x + b)(x + b + c)
Answer : C

Case Based MCQs

Case II : Read the following passage and answer the questions from 43 to 47.
A class teacher decided to organise an educational trip for his class. He asked the students for their preferences, where they want to go.
1/12 th times the square of total number of students want to go to old age home, 7/12 th times the total number of students plan to visit historical  monuments, while 15 students decide to teach children of orphanage home.

Question. Which of the following polynomial represents the above situation, if x is the total number of students?
(a) (7/12)x² + (1/12)x + 15
(b) (1/12)x² + (7/12)x + 15
(c) 7x² + 12x + 15
(d) None of these
Answer : B

Question. The coefficient of x2 in the above polynomial is
(a) 7/12
(b) − 1/12
(c) − 7/12
(d) 1/12
Answer : D

Question. Write the coefficient of x in the polynomial.
(a) − 1/12
(b) 1/12
(c) 7/12
(d) − 7/12
Answer : C

Question. Value of the polynomial at x = 1, is
(a) 172
(b) 150
(c) 176/12
(d) 47/3
Answer : D

Question. Value of the polynomial at x = 2 is
(a) 170/12
(b) 182/12
(c) 190
(d) 33/2
Answer : D
 

1) Find the zeros of the polynomial (a) X2 + 7x + 10 (b) x2 - 25

2) Factorize: a) 9992 - 1 b) (10.2)3 C) 1002 X 998

3) Factorize: a) x3 – 3x2 – 9x – 5 b) x3 + 7x2 – 21x – 27

4) Factorise: (a) 3x2 + 27y2 + z2 - 18xy + 6 √3yz -2 √3zx (b) 27 x3 + 125y3 (c) (2a – 3b + c )2

(d) 1 a3 + b3 + 125 c3 - 15 a b c (e) [x – 1/x y]3 (f) x4 y4 – x y

64 4

(g) 8x3 – (2x – y)3 (h) a6 _ b6

5) Using factor theorem, Show that (a - b) is the factor of a (b2-c2) +b (c2-a2) + c (a2-b2)

6) Factorize: (a) 4√3x2 + 5x - 2√3 (b) 21x2 – 2x + 1/21 (c) 9(2a – b)2 – 4(2a – b) – 13

7) Simplify and factorise (a + b + c)2 _ ( a – b – c )2 + 4b2 – 4c2

8) Factorise: (a2 – b2)3 + (b2 – c2)3 + (c2 – a2)3

9) For what value of a is 2x3 + ax2 + 11x + a + 3 exactly divisible by (2x – 1) (-7)

10) If x – 2 is a factor of a polynomial f(x) = x5 – 3x4 – ax3 + 3ax2 + 2ax + 4, then find the value of a

11) Find the value of a and b so that x2 – 4 is a factor of ax4 + 2x3 – 3x2 + b x – 4 (1, -8)

12) If x = 2 and x = 0 are zeroes of the polynomial 2x3 – 5x2 + p x + b, then find the value of p and b

13) Find the value of a and b so that polynomial x3 –ax2 -13x + b is exactly divisible by (x-1) as well as (x+3) (3, 15)

14) The polynomial x3 – mx2 + 4x + 6 when divided by (x+2) leaves remainder 14 find the value of m

15) If the polynomial ax3 + 3x2 -13 and 2x3 – 5x + a when divided by (x – 2) leave the same remainder, find the Value of a

16) If both (x – 2) and (x – ½) are factors of px2 + 5x + r, show that p = r

17) If f(x) = x4 – 2x3 + 3x2 – ax + b is divided by x-1 and x+1 the remainders are 5 and 19 respectively, then find a and b

18) If A and B be the remainders when the polynomials x3 + 2x2 – 5ax – 7 and x3 + ax2 – 12x + 6 are divided by (x + 1) and (x – 2)

Respectively and 2A + B = 6, find the value of a (2) 19) Show that x +1 and 2x – 3 are factors of 2x3 – 9x2 + x + 12

20) If sum of remainders obtained by dividing ax3 – 3ax2 + 7x + 5 by (x-1) and (x+1) is -36 the find a (22/3)

21) By using suitable identity, find the value of:

(a) (-6)3 + 133+ (-7)3 (b) (-21)3 + (28)3 (c) (9.8)3 – (11.3)3 + (1.5)3 (d) (8/15)3 + (-1/3)3 + (-1/5)3

22) Find the remainder when 9x3 – 3x2 + x – 5 is divided by x – 2

3

23) Find the remainder when x51 + 51 is divided by x + 1 (50)

24) Find the remainder when x3 – px2 + 6x – p is divided by (x – p)

25) Find the value of x3 + y3 + 15xy – 125 when x + y = 5 (0)

26 Find the value of p3 – q3 , if p – q = 5/7 and p q = 7/3 (1840/343)

27) If a + b+ c =8, a2 +b2 + c2 = 30. Find the value of a b + b c + c a (17)

28) If 2x + 3y = 13 and x y = 6 then, find 8x3 + 27y3 (793)

29) Find the value of a3 + b3 +c3 – 3abc, when a + b + c = 8 and a b + b c +c a = 25 (-88)

30) Find the value of x3 + y3 + z3 – 3xyz, if x + y + z = 12 and x2 + y2 + z2 =70 (396)

31) If x + y + z = 1, x y + y z + z x = -1 and xyz = -1, find the value of x3 + y3 +z3 (1)

32) If (a + b)2 = 2a2 + 2b2, show that a = b

33) If (a + b + c) = 0, then prove that a3 + b3 +c3 = 3abc

34) Prove that 2x3 +2y3 + 2z3 – 6xyz =(x + y + z) [(x – y )2 + ( y – z )2 + ( z – x )2 ]

35) Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given

25a2 – 35a + 12

36) Simplify: x + y 3 - x - y 3 (2/15x2y + 2/15y3)

3 5 3 5

37)Simplify : (a + b + c)2 + (a – b + c)2 + ( a + b - c)2

38)What must be subtracted from 4x4 – 2x3 – 6x2 + x – 5, so that the result is exactly divisible by 2x2 + x - 1 (- 6)

39) find the dimensions of a cuboid, whose volume is 2py2 + 6py - 20p

40) If p(x) = x2 – 4x+ 3, evaluate p(2) – p(-1) + p(1/2)

Please click the below link to access CBSE Class 9 Mathematics Worksheet - Polynomials (2)