Class 9 → Mathematics → Polynomials

Q1. The degree of a zero polynomial is:
A0
B1
C2
DNot defined
Q2. The number of terms in the expression 4x²+3x+1 is:
A1
B3
C2
D4
Q3. The number of terms in the expression 4x is
Ax
B4
C1
D2
Q4. The degree of 4 is:
A4
B1
C2
D0
Q5. 7 is an example of:
AConstant polynomial
BLinear polynomial
CBi-quadratic polynomial
DCubic polynomial
Q6. A polynomial of degree 1 is called:
AConstant polynomial
BLinear polynomial
CQuadratic polynomial
DCubic polynomial
Q7. A polynomial of degree 2 is called
AQuadratic polynomial
BBi-quadratic polynomial
CCubic polynomial
DLinear polynomial
Q8. A polynomial of degree 3 is called:
AConstant polynomial
BQuadratic polynomial
CCubic polynomial
DLinear polynomial
Q9. A polynomial of degree 4 is called:
ABi-quadratic polynomial
BQuadratic polynomial
CCubic polynomial
DLinear polynomial
Q10. 5y¹⁰⁰ is a monomial of degree:
A5
By
C100
D1
Q11. 35x³⁵+5 is a binomial of degree
A3
Bx
C5
D35
Q12. 7x³⁵+4x²⁰+5 is a trinomial of degree:
A7
B4
C20
D35
Q13. The coefficient of x² in 2+x²+ x is:
A1
B2
C3
D0
Q14. The coefficient of x³ in πx³+πx²+5 is:
Aπ
B-π
C5
D3
Q15. The degree of 3 is:
A1
B2
C0
D3
Q16. The degree of 7x is:
A7
Bx
C1
D0
Q17. The degree of 0x⁶+3x⁵+0x²+5x+7 is:
A6
B5
C2
D1
Q18. In 2+x-x², the coefficient of x² is:
A2
B1
C-1
D0
Q19. 5y²+3y is a polynomial in the variable:
A5
B3
Cy
DNone of these
Q20. The coefficient of x² in x³+3x²+2 is:
A1
B3
C2
D0
Q21. The coefficient of x in 7x³+5x²+3 is:
A7
B5
C3
D0
Q22. The coefficient of x⁴ in 5x⁵+3x⁴+4x³+2 is
A5
B3
C4
D2
Q23. The degree of x in 2x⁴+-6x+4x+1 is:
A2
B6
C4
D1
Q24. The degree of 7x²+2x+5 is:
A2
B1
C5
D7
Q25. Which of the following is a monomial?
A7x²+5x
B3x³+5x²+5
C0
D10x
Q26. Which of the following is a binomial?
A5x+7
B-4x²+7x+3
C7x
D4x⁴+3x³+2x²+1
Q27. Which of the following is a trinomial?
A0
B3x
C4x+3
D5x²+3x+5
Q28. Which of the following is a constant polynomial?
Ax³+3
Bx+2
Cx³+5x+3
D-4
Q29. 2x+5 is an example of:
AConstant polynomial
BLinear polynomial
CQuadratic polynomial
DCubic polynomial
Q30. 7x³-5x²+3x-9 is an example of:
ACubic polynomial
BQuadratic polynomial
CLinear polynomial
DConstant polynomial
Q31. 3x²+7 is an example of:
ALinear polynomial
BQuadratic polynomial
CCubic polynomial
DNone of these
Q32. The value of the polynomial 5x-4x²+3 at x=0 is:
A0
B3
C-1
D5
Q33. The value of the polynomial 5x-4x²+3 at x=2 is
A-3
B6
C3
D-4
Q34. The coefficient of \( x^3 \) in the expansion of \((2x+1)^3 \) is
A1
B8
C2
D6
Q35. The value of the polynomial 5x-4x²+3 at x=-1 is:
A-3
B-6
C-4
D6
Q36. The value of the polynomial 5x³-2x²+3x-2 at x=1 is:
A-4
B4
C5
D3
Q37. The value of the polynomial 4t²-3t+6 at t=4 is:
A58
B64
C-58
D36
Q38. The value of the polynomial 4t²-3t+6 at t=-5 is:
A121
B112
C-120
D-121
Q39. The number of zeroes in a linear polynomial is:
A3
B2
C1
D0
Q40. Factorizing \(4x^2 + 20x + 25 = 0 \), we get
A\((2 x - 5)^2 \)
B\((4 x+25)^2 \)
C\((4 x-25)^2 \)
D\((2 x+5)^2 \)
Q41. The number of zeroes in a quadratic polynomial is:
A2
B-2
C1
D3
Q42. The number of zeroes in a cubic polynomial is:
A1
B3
C2
D4
Q43. The number of zeroes in a bi-quadratic polynomial is:
A1
B2
C3
D4
Q44. P(0) for the polynomial y²-y+1 is:
A1
B-1
C0
D2
Q45. P(1) for the polynomial y²-y+1 is:
A-1
B1
C0
D2
Q46. P(2) for the polynomial x³ is:
A0
B1
C8
D16
Q47. P(1) for the polynomial 2+t+2t²-t³ is:
A2
B4
C-2
D-4
Q48. The zero of the polynomial x+5 is:
A5
B-5
C0
D1
Q49. The zero of the polynomial x-5 is:
A5
B-5
C0
D1
Q50. The zero of the polynomial 2x+5 is:
A\( \frac{5}{2} \)
B\( \frac{2}{5} \)
C\( \frac{-5}{2} \)
D\( \frac{-2}{5} \)
Q51. The zero of the polynomial 3x-2 is:
A\( \frac{-2}{3} \)
B\( \frac{3}{2} \)
C\( \frac{-3}{2} \)
D\( \frac{2}{3} \)
Q52. The zero of the polynomial 3x is:
A0
B3
C-3
D6
Q53. The zero of the polynomial cx+d is:
A\( \frac{c}{d} \)
B\( \frac{-c}{d} \)
C\( \frac{d}{c} \)
D\( \frac{-d}{c} \)
Q54. The zero of the polynomial 2x+4 is:
A2
B-2
C4
D0
Q55. The zero of the polynomial 4-3x is:
A\( \frac{-4}{3} \)
B\( \frac{4}{3} \)
C\( \frac{3}{4} \)
D\( \frac{-3}{4} \)
Q56. How many zeroes does a zero polynomial have?
A0
B2
CInfinitely many
DNone of these
Q57. How many zeroes does a non-zero constant polynomial have?
ANo zero
BOne zero
CInfinitely many
DNone of these
Q58. The maximum number of zeroes of a polynomial is equal to its:
ANumber of terms
BDegrees
CConstant
DNone of these
Q59. The zero of the polynomial \( \frac{x}{2} \)-3 is:
A6
B-6
C3
D\( \frac{3}{4} \)
Q60. The zero of the polynomial 3x+1 is:
A\( \frac{1}{3} \)
B\( \frac{-1}{3} \)
C3
D-3
Q61. What is the zero of the polynomial 5x-π?
Aπ-5
Bπ+5
C\( \frac{π}{5} \)
D5
Q62. What is the zero of the polynomial x²-1?
A1
B2
C0
D-2
Q63. The zero of the polynomial 2x+1 is:
A\( \frac{1}{2} \)
B2
C1
D\( \frac{-1}{2} \)
Q64. What is the zero of the polynomial 3x²-1?
A\( \frac{3}{√3} \)
B\( \frac{-1}{√3} \)
C\( \frac{2}{√3} \)
D\( \frac{-2}{√3} \)
Q65. The zero of the polynomial lx+m is:
Am-l
B\( \frac{m}{l} \)
C\( \frac{-m}{l} \)
D\( \frac{l}{m} \)
Q66. P(0) of the polynomial (x-1)(x+1) is:
A0
B-1
C3
D2
Q67. P(1) of the polynomial (x-1)(x+1) is:
A0
B1
C2
D-1
Q68. P(2) of the polynomial (x-1)(x+1) is:
A2
B3
C-3
D1
Q69. Which of the following expression is a polynomial in one variable?
A5xy+4yz
B3x²-5x
C5y²+8x
D\( \sqrt{t} \)+3y
Q70. The coefficient of x² in \( \sqrt{2} \)x-1 is:
A1
B2
C0
D-1
Q71. Which of the following is not a polynomial?
A\( \frac{1}{x²} \)+7
B3x
C4x²+5
D7xy+5
Q72. If x + y + z = 0, then \( x^3+y^3+z^3 \) equals
Axyz
B0
Cx + y + z
D3xyz
Q73. \( 7.5^2-2.5^2 \) equals
A50
B500
C5
D5000
Q74. The number of square terms in the expansion of \( (x+y+z)^2 \) is
A3
B2
C6
D4
Q75. The value of \( (-12)^3+5^3+7^3 \)
A420
B-420
C-1260
D1260
Q76. If \( 49x^2-b \) = (7x + \( \frac{1}{2} \)) (7x - \( \frac{1}{2} \)), then the value of b is
A0
B4
C\( \frac{1}{4} \)
D\( \frac{1}{2} \)
Q77. The coefficient of x in the expansion of \( (x+3)^2 \) is
A1
B9
C18
D6
Q78. The number of terms in the expansion of \( (x+y)^3 \) is
A3
B4
C5
D6
Q79. If \( 27y^3+125z^3 \) = p x ( \( 9y^2-15yz+25z^2 \)), then p equals
A3y - 5z
B3y + 5z
Cy + z
Dy - z
Q80. If \( x^2+y^2 \) = -xy, then the value of \( x^3+y^3 \) is
A0
B-1
C1
Dx - y
Q81. The identity (x + a) (x + b) equals
A\( x^2+ab \)
B\( x^2+a+b \)
C(a + b) x
D\( x^2+(a+b)x+ab \)
Q82. If the expansion of \( (3a-2b)^2 \) = \( 9a^2-?+4b^2 \) then ? denotes
A12ab
B3ab
C2ab
D6ab
Q83. The number of terms in the expansion of \( (a+b)^2 \) is
A2
B4
C3
D0
Q84. The expansion of (a + b) (a - b) gives
A\( a^2+b^2 \)
B\( a^2-b^2 \)
C\( (a+b)^2 \)
D\( (a-b)^2 \)
Q85. One of the factors in the expansion of \( (1+64x^3) \) is
A4
B1 + 8x
C8x
D1 + 4x
Q86. The value of \( 51^2-50^2 \) is
A101
B1
C25
D250
Q87. The product of (x + 5) (x + 4) is
A\( x^2+20 \)
B2x + 9
C\( x^2+9x+20 \)
D2x + 20
Q88. The coefficient of \( x^2 \) in the product (3x + 4) (3x - 5)
A3
B9
C20
D-20
Q89. A cubic polynomial can have at the most _________ linear factors.
A0
B1
C2
D3
Q90. If \( 21^2 \) - \( x^2 \) = 41, then x equals
A441
B400
C20
D1
Q91. Which of the following can be the possible factors of the constant term while factorising
6\( x^2 \) + 17x + 5 ?
A2 & 15
B1 & 5
C1 & 17
D10 & 3
Q92. Which of the following expansion gives \( x^2-20x+100 \)?
A\( x^2-10^2 \)
B\( (x+10)^2 \)
C\( (x-10)^3 \)
D\( (x-10)^2 \)
Q93. On factorising \( 4y^2+4y+1 \), we get
A\( (2y-1)^2 \)
B\( (2y+1)^2 \)
C\( (4-y)^2 \)
D\( (4+y)^2\)
Q94. Jack has a cuboidal block whose volume is given by 4\( x^6 \) - 20x. One of the possible dimensions of this cuboid is
A\( x^6 \), 4 & 20
B×, ( ×+ 20) & 4
C×, (× - 4) & 20
D4, × & (× - 5)
Q95. Which identity is applicable to factorise \( x^3-8y^3-6x^y+12xy^2 \)
A\( (x+y)^3 \)
B\( x^3-y^3 \)
C\( (x-y)^3 \)
D\( x^3+y^3 \)
Q96. If a + b =10 and ab = 21, the value of \( a^3+b^3 \) is
A10
B20
C370
D210
Q97. x + 2 is a factor of
A\( x^2-4 \)
B\( x^2-2 \)
C\( x^2+4 \)
D\( x^2+2 \)
Q98. x³-2x²+16 is divisible by:
Ax-2
Bx+2
Cx+1
Dx-1
Q99. If the factorisation of x²+x-6=(x-2)(x+a), then 'a' equals:
A1
B-3
C3
D6
Q100. The term containing \( a^2b \) in the expanded form of \( (2a-b)^3 \) is
A\( -12a^2b \)
B\( 6a^b \)
C\( 8a^2b \)
D\( -6a^b \)
Q101. \( x^2+y^2+z^2-2xy+2yz-2zx \) is the expanded form of
A\( (x+y+z)^2 \)
B\( (x-y-z)^2 \)
C\( (x+y-z)^2 \)
D\( (x-y+z)^2 \)
Q102. One of the factors of \( 512m^3-343n^3 \) is
A64m +49n
B6m - 7n
C8m - 7n
Dm - n
Q103. On factorising \( \sqrt{2} \)x²+3x+\( \sqrt{2} \), we get
A(x-\( \sqrt{2} \))(\( \sqrt{2} \)x+1)
B(x-2)(x+2)
C(x+\( \sqrt{2} \))(x+2)
D(x+\( \sqrt{2} \))(\( \sqrt{2} \)x+1)
Q104. The value of \( (0.2)^3-(0.3)^3+(0.1)^3 \) is
A18
B-18
C-0.018
D0.18
Q105. If x²-5x+6=(x-2)×p, then p=?
Ax-3
Bx-5
Cx-6
Dx-1
Q106. \( (x^2+8x+16) \) is the square of
Ax + 4
Bx +8
Cx + 16
Dx +2
Q107. If x⁵¹+2x⁶⁰+3x+2 is divisible by (x+1), then p(1) is:
A1
B0
C-1
D60
Q108. Which identity can be used to find the product 101 x 99?
A\( x^2+y^2 \)
B(x + a) (x + b)
C(a + b) (a - b)
D\( (a+b)^2 \)
Q109. Joanna's grandmother decided to knit her a scarf on her birthday. Joanna told her that the area if handkerchief should be (x²-10x+21) and it's length to be (x-3). Why should be the width of the scarf?
A(x+7)
B(x+3)
C(x-7)
D(x-10)
Q110. (× + 6) is one of the factor of
A\( x^6 \) + 9× + 18
B\( x^6 \) - 9× +18
C\( x^6 \) - 9× - 18
D\( x^6 \) + 9× + 6
Q111. The identity suitable to evaluate \( (103)^3 \) is
A\( (x+y)^3 \)
B\( x^3-y^3 \)
C\( (x-y)^3 \)
D\( x^3+y^3 \)
Q112. If the factorisation of x³-23x²-142x-120=(x-p)(x-10)(x-12), then the value of p is:
A2
B3
C1
D0
Q113. If (× + 1) is a factor of 2\( x^6 \) + k×. Then the value of k is
A-3
B2
C4
D-2
Q114. The identity suitable to find the product of 105×95 is:
Aa²-b²
B(a-b)
C(a+b)²
DAll of the above
Q115. The value of (888)²-(112)² is:
A776
B1000
C776000
D1776
Q116. The factorisation of 4\( x^6 \) + 8× + 3 is
A(× + 1) (× + 3)
B(2× + 1) (2× + 3)
C(2× + 2) (2× + 5)
D(2× - 1) (2× - 3)
Q117. Which of the following polynomial has (x -2) as a factor?
A\( 3x^2-6x+24 \)
B\( 3x^2+6x-24 \)
C\( 4x^2+x-2 \)
D\( 4x^2-x-2 \)
Q118. Which of the following can be the possible factors of x³-6x²+3x+10?
A(x+1)(x-3)(x-5)
B(x+1)(x+3)(x-5)
C(x+1)(x+4)(x-5)
D(x+1)(x-2)(x-5)
Q119. The common factor \( x^3 \) - \( x^2 \) and \( x^4 \) - \( x^3 \) is
A(× + 1)
B\( x^3 \)
C(× - 1)
D\( x^4 \)
Q120. Polynomial x³-4x²+x+6 can be factorised into:
A6 factors
B3 factors
C4 factors
D1 factor
Q121. The value of k if (x - 2) is a factor of \( x^3-3x^2+5x-k \)
A6
B3
C2
D4
Q122. The value of k for which (x-1) is a factor of kx²-3x+k is:
A2
B3
C\( \frac{2}{3} \)
D\( \frac{3}{2} \)
Q123. If (x - a) is a factor of p(x), then
Ap(-a) = 0
Bx = 0
Cp(a) = 0
Da = 0
Q124. Find the factor of the expression ab + bc + a× + c×.
A(a + c)
B(× + a)
C(a + b)
D(a + c)
Q125. The common factors of ax²+ax and bx²+bx is:
Ax(x+1)
Ba(x+1)
COnly x
DOnly (x+1)
Q126. If g(x)=x-1 is a factor of p(x), then the value of p(1) is:
A1
B-1
C2
D0
Q127. Which of the following is a factor of p¹⁰⁰-1?
Ap-100
Bp-1
Cp+1
Dp+100
Q128. For any polynomial p(x), if p(a) = 0, then which one is true?
A(x + a) is a factor
B(x - a) is a factor
Ca = 0
Dnone of the above
Q129. To factorise a\( x^2 \) + bx + c, by splitting the middle term, we write 'b' as the
Asum of two numbers whose product is c
Bsum of two numbers whose product is 'ac'
Cdifference of two numbers whose product is 'ac'
Dnone of the above
Q130. One of the factors of (25x²-1)+(1+5x)² is:
A5+x
B5-x
C5x-1
D10x
Q131. If (x - 1) is a factor of p(x) = \( x^2+x+k \), then k = ?
A0
B1
C2
D-2
Q132. To factorise 2\( x^2 \) - × - 6. The factors taken are
A1 & 6
B2 & 3
C3 & 4
D6 & 2
Q133. Which of the following is a factor p(x) = \( 2x^3+x^2-2x-1 \) ?
Ax + 2
Bx - 2
Cx +1
Dx - 1
Q134. If 2x-3 is a factor of x+2x³-9x²+12, then by factor theorem,
Ap(2)=0
Bp(3)=0
Cp(\( \frac{3}{2} \))=0
Dp(\( \frac{2}{3} \)=0
Q135. On factorising \( x^2+5x-66 \), we get one of its factors as
Ax - 11
Bx + 6
Cx + 11
Dx - 66
Q136. If x + 2 is a factor of \( x^3 \) + 3 \( x^2 \) + 5× + 6, then p(-2) =
A0
B1
C-2
D2
Q137. One possible factor of \( x^3 \) + \( x^2 \) + × + 1 is
A0
B× + 3
C× + 2
D× + 1
Q138. When a polynomial p(x) is divided by g(x) to give q(x) as quotient and remainder r(x), which one of the following is true?
Ap(x) = q(x) x r(x) + g(x)
Bp(x) = g(x) x q(x) + r(x)
Cp(x) = g(x) x q(x) x r(x)
Dp(x) = g(x) + r(x)
Q139. The constant term in the expansion of \( (3x-4)^2 \) is
A9
B12
C4
D16
Q140. The factors of \( x^ 2-3x -10\) is
A(x+2) (x-5)
B(x - 2) (x + 5)
C(x - 2) (x - 5)
D(x + 2) (x + 5)