POLYNOMIALS NCERT 9 MATHEMATICS TEXTBOOK MCQ (Multiple Choice Questions)

Q1. If p(x) = 7 – 3x + 2x2 then value of p(-2) is:

  1. 12
  2. 31
  3. 21
  4. 22

Q2. In the division of a cubic polynomial p(x) by a linear polynomial, the remainder is p(-2). So, the divisor must be

  1. x – 2
  2. x + 2
  3. 2x + 1
  4. 2x – 1  

Q3. If p(x) = 2x2 – 3x + 1 does not have  x – a as a factor, then p(a) 

  1. is equal to zero
  2. is a non zero number
  3. is 4a – 1
  4. is 4a + 1

Q4. If (x – 2) is a factor of x+ 2x + a, find the value of ‘a’.

  1. a = -8
  2. a = 8
  3. a = -16
  4. a = 16

Q5.   p(x) is a polynomial in x, ‘a’ is a real number. If (x – a) is a factor of p(x), then p(a) must be

  1. positive
  2. negative
  3. zero
  4. 2a

Q6. What is the remainder when q(x) = 2x3 – x2 + x – 1 is divided by x + 2?

  1. 20
  2. – 23
  3. 35
  4. – 32

Q7. Evaluate (11)3

  1. 1331
  2. 3113
  3. 1313
  4. 3131

Q8. Factorise the polynomial  x2n+ 5xn + 6

  1. (xn– 3) (xn– 2)
  2. (xn+ 3) (xn– 2)
  3. (xn– 3)xn+ 2)
  4. (xn+ 3)(xn+ 2)

Q9. The degree of the polynomial x4 – 3x3 + 2x2 – 5x + 3 is:

  1. 4
  2. 2
  3. 3
  4. 1

Q10. Find the coefficients of x2 in x2 – 2x + 4

  1. – 2
  2. 2
  3. 1
  4. -1

Q11. For a polynomial p(x) when divided by x + 3 leaves a remainder of 2. So, which of the following is true?

  1. p(-3) = 2  
  2. p(2) = -3  
  3. p(3) = 2  
  4. p(-2) = 3

Q12. Factorise: x7y + xy7

  1.  xy(x– y2)(x+ y– x2y2
  2.  xy(x+ y2)(x+ y– x2y2)
  3.  xy(x+ y2)(x– y+ x2y2)
  4. xy(x– y2)(x– y+ x2y2)

Q13. In 3z3 – 9x6 – 6y4 + z, the degree of the polynomial is 

  1. 1
  2. 3
  3. 4
  4. 6

Q14. Factorisation by splitting the middle term: 24x2 – 65x + 21

  1.  (3x + 7)( 8x – 3)
  2. (3x – 7)( 8x – 3)
  3. (3x – 7)( 8x+ 3)
  4. (3x + 7)( 8x+ 3)

Q15. A linear polynomial will have how many zeroes.

  1. 1  
  2. 2
  3. 3
  4. 0

Q16. On dividing f(x) = 2x− 9x3 − 21x+ 88x + 48 by (x − 2), we get the remainder 

  1. 50
  2. 150
  3. 100
  4. 75

Q17. Evaluate 1043

  1. 1124864
  2. 1142846
  3. 1124844
  4. 1142864

Q18. Factorise: x4-1

  1.    (x2+1)(x- 1) (x+1)
  2.    (x2-1) (x-1)(x+1)
  3.    (x2+1)(x- 1)(x-1)
  4.    (x2+1) (x+1)(x+1)

Q19. Find the value of p such that (x – 1) is the factor of the polynomial x+ 10x+ px.

  1. p = 7
  2. p = -7
  3. p = -11
  4.  p = 11

Q20. In 5y2 + 8y – 3y3, 8 is the coefficient of 

  1. y
  2. y2
  3. y3
  4. y + 1

Q21. What is remainder when x3 – 2x2 + x + 1 is divided by (x -1)?

  1. 0
  2. -1
  3. 1
  4. 2

Q22. In −1x + 2y = z, what are the variables? 

  1. −1, x, y
  2. −1, 2, −1
  3. x, y, z
  4. −1, 2, 1

Q23.  Find the remainder when p(x) = x2 – 2x is divided by x – 2.

  1. 1
  2. 0
  3. – 1
  4. 2

Q24. The degree of a non-zero constant polynomial is always 

  1. 0
  2. 1
  3. −1
  4. 2

Q25. 8x3 – 343y= ?

  1. (2x-7y) (4x2 + 14xy + 49y2)
  2. (2x+7y)(4x2 – 14xy + 49y2)
  3. (2x + 7y) (2x – 7y)
  4. (2x – 7y) (4x2 – 49y2)

Q26. If 3a – 7b = 26 and ab = 5, then  the value of 9a2 + 49b2.

  1. 516
  2. 872
  3. 886
  4. 643

Q27. Factorise: x2– 81

  1.     (x-9)(x-9)
  2.     (x-9)(x+9)
  3.     (x-81)(x+1)
  4.     (x+9)(x+9)

Q28. For a polynomial p(x) = 2x4 – 3x3 + 2x2 + 2x – 1, what is the remainder when it is divided by x + 4?

  1. p(4)
  2. p(-2)
  3. p(- 4)
  4. p(2)

Q29. Find the value of p(2) if p(x) has (x – 2) as its factor.

  1. 0
  2. 2
  3. -2
  4. 3

Q30. If x – 2 is a factor of ax– x – 6, then what should be the value of a?

  1. 3
  2.  4
  3.  2
  4.  1

Q31. In y6 − 10y4 − 12y3 + 1, the coefficient of y3 is 

  1. 1
  2. −10
  3. −12
  4. −1

Q32. One of the factors of (16y2 – 1) + (1 – 4y)2 is

  1. (4 + y)
  2. (4 – y)
  3. (4y + 1)
  4. 8y

Q33. What is the remainder when x− 12x2 − 42 is divided by x − 3? 

  1. 245
  2. 123
  3. 344
  4. -123

Q34. The term mxn… m is 

  1. a natural number
  2. a whole number
  3. an integer
  4. a real number

Q35. Degree of the polynomial p(x) = 4x4 + 2x3 + x5 + 2x + 7 is:

  1. 7
  2. 4
  3. 5
  4. 3

Q36. A linear polynomial is a polynomial of degree ……….

  1. 1  
  2. 2
  3. 0
  4. 3

Q37. Evaluate: (102)2

  1.   10444
  2.   10404
  3.   10044
  4. 10440

Q38. What is the coefficient of x in x3 + 3x2 – 2x – 1?

  1. -2
  2. 1  
  3. 3  
  4. -1  

Q39. Find the value of (12m – 15n) 2

  1. 122m2 – 360mn + 225n2
  2. 144m2 – 180mn + 225n2
  3. 144m2 – 360mn + 225n2
  4. 144m2 + 360mn + 125n2

Q40. Factorize: 125a3 – 27b3 – 225a2b + 135ab2.

  1. (5a + 3b) (5a – 3b) (5a + 9b)
  2. (3a – 5b) (3a – 5b) (3a – 5b)
  3. (5a – 3b) (5a – 3b) (5a – 3b)
  4. (3a – 5b) (5a – 3b) (3a + 5b) 2

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