CBSE Class 9 Maths Polynomials MCQs

Question. In 2 + x + x² the coefficient of x² is:
(a) 2
(b) 1
(c) – 2
(d) –1

Question. In 2 – x² + x³ the coefficient of x² is:
(a) 2
(b) 1
(c) – 2
(d) –1

Question. In πx²/2 +x+10  the coefficient of x² is:
(a)  π/2
(b) 1
(c) – π/2
(d) –1

Question. The degree of 5t – 7 is:
(a) 0
(b) 1
(c) 2
(d) 3

Question. The degree of 4 – y² is:
(a) 0
(b) 1
(c) 2
(d) 3

Question. The degree of 3 is:
(a) 0
(b) 1
(c) 2
(d) 3

Question. The value of p(x) = 5x – 4x² + 3 for x = 0 is:
(a) 3
(b) 2
(c) – 3
(d) – 2

Question. The value of p(x) = 5x – 4x² + 3 for x = – 1 is:
(a) 6
(b) –6
(c) 3
(d) – 3

Question. The value of p(x) = (x – 1)(x + 1) for p(1) is:
(a) 1
(b) 0
(c) 2
(d) – 2

Question. The value of p(t) = 2 + t + 2t² – t³ for p(0) is:
(a) 1
(b) 2
(c) – 1
(d) 3

Question. The value of p(t) = 2 + t + 2t² – t³ for p(2) is
(a) 4
(b) –4
(c) 6
(d) 7

Question. The value of p(y) = y² – y +1 for p(0) is:
(a) –1
(b) 3
(c) –2
(d) 1

Question. (x + 8)(x – 10) in the expanded form is:
(a) x² – 8x – 80
(b) x² – 2x – 80
(c) x² + 2x + 80
(d) x² – 2x + 80

Question. The value of 95 x 96 is:
(a) 9020
(b) 9120
(c) 9320
(d) 9340

Question. The value of 104 x 96 is:
(a) 9984
(b) 9624
(c) 9980
(d) 9986

Question. Without actual calculating the cubes the value of 28³ + (–15)³ +(–13)³ is:
(a) 16380
(b) –16380
(c) 15380
(d) –15380

Question. If x – 2 is a factor of x³ – 2ax² +ax – 1 then the value of a is:
(a) 7/6
(b) –7/6
(c) 6/7
(d) 6/7

Question. If x + 2 is a factor of x³ + 2ax² +ax – 1 then the value of a is:
(a) 2/3
(b) 3/5 
(c) 3/2
(d) 1/2

Question. If x + y + z = 0 then x³ + y³ + z³ is equal to
(a) 3xyz
(b) – 3xyz
(c) xy
(d) –2xy

Question. The factors of 2x² – 7x + 3 are:
(a) (x – 3)(2x – 1)
(b) (x + 3)(2x + 1)
(c) (x – 3)(2x + 1)
(d) (x + 3)(2x – 1)

Question. The factors of 6x² + 5x – 6 are:
(a) (2x – 3)(3x – 2)
(b) (2x – 3)(3x + 2)
(c) (2x + 3)(3x – 2)
(d) (2x + 3)(3x + 2)

Question. The factors of 3x² – x – 4 are:
(a) (3x – 4)(x – 1)
(b) (3x – 4)(x + 1)
(c) (3x + 4)(x – 1)
(d) (3x + 4)(x + 1)

Question. The factors of 12x² – 7x + 1 are:
(a) (4x – 1)(3x – 1)
(b) (4x – 1)(3x + 1)
(c) (4x + 1)(3x – 1)
(d) (4x + 1)(3x + 1)

Question. The factors of x³ – 2x² – x + 2 are:
(a) (x – 1)(x – 1)(x – 5)
(b) (x + 1)(x + 1)(x + 5)
(c) (x + 1)(x – 1)(x + 5)
(d) (x + 1)(x + 1)(x – 5)

Question. Which of the following is not a polynomial?
(a) x² +√2x+3
(b) x²+ √2x+6
(c) x³+3x²+3
(d) 6x+4

Question. The degree of the polynomial 3x³ – x⁴ + 5x + 3 is
(a) –4
(b) 4
(c) 1
(d) 3

Question. Zero of the polynomial p(x) = a²x, a≠0 is
(a) x = 0
(b) x = 1
(c) x = –1
(d) a = 0

Question. Which of the following is a term of a polynomial?
(a) 2x
(b) 3/x
(c) x^√x
(d) x

Question. If p(x) = 5x² – 3x + 7, then p(1) equals
(a) –10
(b) 9
(c) –9
(d) 10

Question. Factorisation of x³ + 1 is
(a) (x + 1)(x² – x + 1)
(b) (x + 1)(x² + x + 1)
(c) (x + 1)(x² – x – 1)
(d) (x + 1)(x² + 1)

Question. If x + y + 2 = 0, then x³ + y³ + 8 equals
(a) (x + y + 2)³
(b) 0
(c) 6xy
(d) –6xy

Question. If x = 2 is a zero of the polynomial 2x² + 3x – p, then the value of p is
(a) –4
(b) 0
(c) 8
(d) 14

Question. x+1/x is
(a) a polynomial of degree 1
(b) a polynomial of degree 2
(c) a polynomial of degree 3
(d) not a polynomial

Question. Integral zeroes of the polynomial (x + 3)(x – 7) are
(a) –3, –7
(b) 3, 7
(c) –3, 7
(d) 3, –7

Question. The remainder when p(x) = 2x² – x – 6 is divided by (x – 2) is
(a) p(– 2)
(b) p(2)
(c) p(3)
(d) p(–3)

Question. If 2(a²+b²)=(a+b)² , then
(a) a + b = 0
(b) a = b
(c) 2a = b
(d) ab = 0

Question. If x³ + 3x² + 3x + 1 is divided by (x + 1), then the remainder is
(a) –8
(b) 0
(c) 8
(d) 1/8

Question. The value of (525)² – (475)² is
(a) 100
(b) 1000
(c) 100000
(d) –100

Question. If a + b = –1, then the value of a³ + b³ – 3ab is
(a) –1
(b) 1
(c) 26
(d) –26

Question. The value of (2 - a)³ + (2 - b)³ + (2 - c)³ - 3(2 - a)(2 - b)(2 - c) when a + b + c = 6 is
(a) –3
(b) 3
(c) 0
(d) –1 

Question. The number of zeroes of the polynomial x³ + x – 3 – 3x² is
(a) 1
(b) 2
(c) 0
(d) 3

Question. If (x + 2) and (x – 2) are factors of ax⁴ + 2x – 3x² + bx – 4, then the value of a + b is
(a) –7
(b) 7
(c) 14
(d) –8

1. A combination of constants and variables connected by +, –, × and ÷ is known as an algebraic expression.
e.g., 2 – 3x + 5x–2 y–1 + 1/3 x/y³

2. An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial.
e.g., 2 – 3x + 5x²y –1/3 xy³

3. In the case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial.
e.g., 5x² – 7x + 3/2 is a polynomial in x of degree 3.

4. In the case of polynomials in mor than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial.
e.g., 5x³ – 2x²y² – 3x²y + 9y is a polynomial of degree 4 in x and y.

5. A polynomial of degree 1 is called a linear polynomial.

6. A polynomial of degree 2 is called a quadratic polynomial.

7. A polynomial of degree 3 is called a cubic polynomial.

8. A polynomial of degree 4 is called a biquadratic polynomial.

9. A polynomial containing 1 term is called a monomial.

10. A polynomial containing 2 terms is called a bionomial.

11. A polynomial containing 3 terms is called a trinomial.

12. A polynomial containing one term consisting of a constant is called a constant polynomial.

13. The degree of a constant polynomial is zero.

14. The terms of a polynomial are said to be in ascending (or) descending order if they increase (or decrease in degrees respectively.
e.g., (i) 3 – 7x + 5x² – 2x³ is in ascending order
(ii) – 2x³ + 5x² – 7x + 3 is in descending order.

15. Terms with same variables and which have the same exponents are called like or similar terms, otherwise they are called unlike (or) dissimilar terms.
e.g., (i) 3x³, 1/2x³ , – 9x³, ....etc, are like terms.
(ii) x²y, 3xy², – 4x³, ... etc are unlike terms.

16. Dividend = (divisor × quotient) + reminder.

Question. If (x–2) is one factor of x² + ax – 6 = 0 and x² – 9x + b = 0 then a+b =
(A) 15
(B) 13
(C) 11
(D) 10

Answer: A

Question. The remainder obtained when t6 + 3t² + 10 is divided by t³ + 1 is
(A) t² – 11
(B) t³ – 1
(C) 3t² + 11
(D) none

Answer: C

Question. The value of the product (3x² – 5x + 6) and (–8x³) when x = 0 is
(A) ½
(B) 2
(C) 1
(D) 0

Answer: D

Question. The difference of the degrees of the polynomials 3x²y³ + 5xy⁷ – x⁶ and 3x⁵ – 4x³ + 2 is
(A) 2
(B) 3
(C) 1
(D) none

Answer: B

Question. What must be added to x² + 5x – 6 to get x³ – x² + 3x – 2?
(A) x³ – x² + 3x – 2
(B) x³ – 2x² – 2x – 4
(C) x³ – 2x – 2x + 4
(D) none

Answer: C

Question. What must be subtracted from x⁴ + 2x² – 3x + 7 to get x³ + x² + x – 1?
(A) x⁴ – x³ + x² – 4x + 8
(B) x³ + x² – 4x + 8
(C) x⁴ – x³ + x² + 4x – 8
(D) x⁴ – x³ – x² + 4x – 8

Answer: A

Question. The product of x²y and x/y is equal to the quotient obtained when x2 is divided by
(A) 0
(B) 1
(C) x
(D) 1/x

Answer: D

Question. If (3x – 4) (5x + 7) = 15x² – ax – 28 then a =
(A) 1
(B) – 1
(C) – 2
(D) none

Answer: B

Question. The product of two factors with unlike signs is
(A) positive
(B) negative
(C) cannot be determined
(D) none of these

Answer: B

Question. Subtract x³ – xy² + 5x²y – y³ from –y3 –6x²y – xy² + x³
(A) 2y³ – 8x²y + 3xy² – 2x³
(B) 2x³ – 2xy² – x²y – 2y³
(C) – 11x²y
(D) none of these

Answer: C

Question. Which of the following expressions is a polynomial?
(A) 3x^{1/ 2} - 4x +3
(B) 4x² -√3 x + 5
(C) 3x² y - 2xy + 5x⁴
(D) 2x⁴ + 3/x² - 1

Answer: C

Question. The degree of the polynomial 5x³ – 6x³y + 4y² – 8 is
(A) 3
(B) 4
(C) 2
(D) can’t be determined

Answer: B

Question. What must be added to x³ + 3x – 8 to get 3x³ + x² + 6?
(A) 2x³ + x² – 3x + 14
(B) 2x² + x² + 14
(C) 2x³ + x² – 6x – 14
(D) none of these

Answer: A

Question. What must be subtracted from x³ – 3x² + 5x – 1 to get 2x³ + x² – 4x + 2?
(A) – x³ + 4x² – 9x + 3
(B) x³ + 4x² – 9x + 3
(C) x³ – 4x² + 9x – 3
(D) – x³ – 4x² + 9x – 3

Answer: D

Question. Divide (– 56 mnp²) by (7 mnp)
(A) – 8p
(B) 8 mnp
(C) 8 p
(D) none

Answer: A

Question. A factor of x³ – 1 is
(A) x – 1
(B) x² + x + 1
(C) either A or B
(D) none of these

Answer: C

Question. The product of 2/3 xy by 3/2 xz is 
(A) 1/6 xyz
(B) x²yz
(C) 6 x²yz
(D) none of these

Answer: B

Question. Divide 8x²y² – 6xy² + 10x²y³ by 2xy
(A) 4xy – 3y + 5xy²
(B) 4xy + 3y – 5xy²
(C) 8xy + 3y – 5xy²
(D) 4xy – 3y – 5xy²

Answer: A

Question. The product of (x² + 3x + 5) and (x² – 1) is
(A) x⁴ + 3x³ – 4x² – 3x – 5
(B) x⁴ + 3x³ + 4x² – 3x – 5
(C) x⁴ + 3x³ + 4x² + 3x – 5
(D) none of these

Answer: B

Question. If quotient = 3x² – 2x +1, remainder = 2x – 5 and divisor = x + 2 then the dividend is
(A) 3x³ – 4x² + x – 3
(B) 3x³ – 4x² – x + 3
(C) 3x³ + 4x² – x + 3
(D) 3x³ + 4x² – x – 3

Answer: D

Question. If 0 < a < 1, then the value of a+1/a is
(A) Greater than 2
(B) Less than 2
(C) Greater than 4
(D) Less than 4

Answer: A

Question. The value of (0.31)³ - (0.21)³/0.0961 0.0651 0.0441 is
(A) 0
(B) 0.1
(C) 0.2
(D) 0.04

Answer: B

Question. The remainder obtained when x⁶ + 3x² + 10 is divided by x³ + 1 is
(A) x² – 11
(B) x³ – 1
(C) 3x + 11
(D) x³ + x

Answer: C

Question. The value of the product (3+5/x)(9-15/x + 25/x²) at x = 1 is
(A) 150
(B) 148
(C) 152
(D) 140

Answer: C

Question. (9p – 5q)² + 180 pq is equivalent to
(A) (5p + 9q)²
(B) (5p – 9q)²
(C) (9p + 5q)²
(D) (9p – 6q)²

Answer: C

Question. (3x – 5q)³ – (5x – 2y)³ + (2x + 3y)³ is equal to
(A) (3x – 5y) (5x – 2y) (2x + 3y)
(B) 3(3x – 5y) (4x – 2y) (2x + 3y)
(C) (3x – 5y) (2y – 5x) (2x + 3y)
(D) –3(3x – 5y) (5x – 2y) (2x + 3y)

Answer: D

Question. The inequality b² + 5 > 9b + 12 is satisfied by
(A) b> 9 (or) b < 1
(B) b > 9 (or) b < 0
(C) b = 10 (or) b = –1
(D) b > 8 (or) b < 0

Answer: C

Question. If a + b + c = 9 and ab + bc + ca = 26, then the value of a³ + b³ + c³ – 3abc is
(A) 27
(B) 39
(C) 495
(D) 729

Answer: A

Question. The quotient when 8x2y² + 6xy² + 10x²y³ is divided by 2xy is
(A) 4xy – 3y + 5xy²
(B) 4xy + 3y – 5xy²
(C) 8xy + 3y – 5xy²
(D) 4xy – 3y – 5xy²

Answer: A

Question. The value of (x + 3)³ – (x – 3)³ is
(A) 0
(B) 1 – x³
(C) 3x² – 5
(D) 18x² + 54

Answer: D

Question. The product of (4x – 3y) and (16x² + 12xy + 9y²) is
(A) (4x – 3y)³
(B) (16x² + 12xy + 9y2)²
(C) 64x³ – 27y³
(D) (x – y)²

Answer: C

Question. If x²+1/x² = 79 , then x+1/x = ____
(A) √75
(B) 9
(C) √79
(D) 8

Answer: B

Question. If a + b + c = 10 and a² + b² + c² = 36 then ab + bc + ca =.......
(A) 136
(B) 64
(C) 32
(D) 68

Answer: C

Question. If x – y = 4 and xy = 21, then x³ – y³ =
(A) 361
(B) 316
(C) –188
(D) 360

Answer: B

Question. The product of 2/3 xy by 3/2 xz is 
(A) 1/6 xyz
(B) x²yz
(C) 6x²yz
(D) xyz

Answer: B

Question. Which of the following is not a polynomial is x ?
(A) √3x² + √2 √x + 5
(B) x² - 5x + 6
(C) x⁴ + 5x³ – 2 √3x + 8
(D) 3x + 11

Answer: A

Question. The degree of constant polynomial is ....
(A) 1
(B) 2
(C) 0
(D) 3

Answer: C

Question. If x - 1/2 = √6 , then x² + 1/x² = __
(A) 2
(B) 4
(C) 6
(D) 8

Answer: D

Question. The quotient when (–56 mnp²) is divided by (7 mnp) is
(A) –8p
(B) 8 mnp
(C) 8 p
(D) 8 m

Answer: A

Question. On dividing 8x²y² by –2xy, we get quotient
(A) –4xy²
(B) 4xy²
(C) 4x²y³
(D) 4xy

Answer: A

Question. If 3x – 7y = 10 and xy = –1, then the value of 9x² + 49y² is
(A) 58
(B) 142
(C) 104
(D) –104 

Answer: A

Question. The value of (67.542)² - (32.458)²/75.458 40.374
(A) 1
(B) 10
(C) 100
(D) 20

Answer: C

Question. If 2x + y = 5, then 4x + 2y is equal to
(A) 5
(B) 8
(C) 9
(D) 10

Answer: D

Question. On dividing 29x – 6x² – 28 by 3x – 4, we get quotient
(A) –2x + 7
(B) 2x – 7
(C) 2x + 7
(D) 2x

Answer: A

Question. If (0.42)³ + (0.25)³ + (0.33)^{3 -} 3 x 0.42 x 0.25 x 0.33 / (0.42)² + (0.25)² + (0.33)² - 0.42 x 0.25 - 0.25 x 0.33 - 0.33 x 0.42 then the value of y is
(A) 1
(B) 0
(C) 1/2
(D) 2 

Answer: A

Question. If the product of two numbers is 10 and the sum is 7, then the larger of the two numbers is
(A) –2
(B) 2
(C) 5
(D) 4. 1/4

Answer: C

Question. Find the missing term in the following problem 

(A) 2xy
(B) –2xy
(C) 12xy
(D) –12xy

Answer: B

Question. The value of 7.83 x 7.83 - 1.17 x 1.17 /6.66 is
(A) 9
(B) 6.66
(C) 1.176
(D) 8

Answer: A

Question. On multiply 7x² by – 6x³, we get product
(A) 42x6
(B) –42x
(C) –42x⁵
(D) 40x

Answer: C

Question. If x³ + y³ + z³= 3xyz, then the relation between x, y and z is
(A) x + y + z = 0
(B) x = y = z
(C) Either x + y + z = 0 or x = y = z
(D) Neither x + y + z = 0 nor x = y = z

Answer: C

Question. The degree of polynomial 6x³ + 7x² + 10 is ....
(A) 3
(B) 2
(C) 1
(D) 4

Answer: A

Question. The factors of y² + 3y + y + 3 are
(A) (y + 1) (y + 3)
(B) y² + 32
(C) (y² + 3)²
(D) (y + 2) (y + 1)

Answer: A

Question. 

 

Answer: B

Question. If x+1/x = √5 , then the value of x³+1/x³ is
(A) 8 √5
(B) 2 √5
(C) 5 √5
(D) 7√5

Answer: B

Question. The factors of (1 – 6z + 9z²) are
(A) (1 + 3z)(1 – 3z)
(B) (z + 3)²
(C) (3z – 1)²
(D) (z – 3)²

Answer: C

Question. The factors of x² - 2 √3x + 3 are
(A) (x + √3)²
(B) (x - √3)²
(C) (x + √3)(x - √3)
(D) (x + 2)(x + √3)

Answer: B

Question. The factors of (a⁴b⁴ – 16c⁴) are
(A) 4(a²b² + c² )(ab - 2c)(ab + 2c)
(B) (a²b² - 4c² )(ab + 2c)²
(C) (a²b² + 4c² )(ab + 2c)(ab - 2c)
(D) (a²b² - 4c² )2(ab + 2c)(ab + 4c)

Answer: C

Question. If ‘a’ is an integer such that a+1/a = 17/4 , then the value of (a - 1/a) is
(A) 4
(B) 13/4
(C) 17/4
(D) 15/4

Answer: D

Question. The factors of (a² – b² – 4ac + 4c²) are
(A) (a + 2c + b)(a - 2c - b)
(B) (a - 2c + b)(a - 2c - b)
(C) (a - 2c + c)(a + b + 2c)
(D) (a - 2b)(a + 2b + 2c)

Answer: B

Question. The factors of (x² – 1 – 2a²) are
(A) (x - a -1)(x + a +1)
(B) (x - a +1)(x + a +1)
(C) (x + a +1)(x + a -1)
(D) (x + a -1)(x - a +1)

Answer:  A

Question. What is the remainder when (4x² – 3x² + 2x – 1) is divided by (x + 2)?
(A) 49
(B) 48
(C) – 49
(D) – 48

Answer: C

Question. The zero of p(x) = 2x – 7 is:
(a) 7/2
(b) 2/7
(c) –2/7
(d) –7/2

Question. The zero of p(x) = 9x + 4 is:
(a) 4/9
(b) 9/4
(c) –4/9
(d) –9/4

Question. Which are the zeroes of p(x) = x² – 1:
(a) 1, –1
(b) – 1, 2
(c) –2, 2
(d) –3, 3

Question. Which are the zeroes of p(x) = (x – 1)(x – 2):
(a) 1, –2
(b) – 1, 2
(c) 1, 2
(d) –1, –2

Question. Which one of the following is the zero of p(x) = lx + m
(a) m/l
(b) l/m
(c) – m/l
(d) – l/m

Question. Which one of the following is the zero of p(x) = 5x–∏ :
(a) – 4/5π 
(b) 1/5π 
(c) 4/5π  
(d) none of these

Question. On dividing x³ + 3x² + 3x +1 by x we get remainder:
(a) 1
(b) 0
(c) – 1
(d) 2

Question. On dividing x³ + 3x² + 3x +1 by x+π we get remainder:
(a) -π³+3π²-3π+1
(b) π³-3π²-3π+1
(c) -π³+3π²-3π-1
(d) -π³+3π²-3π-1

Question. On dividing x³ + 3x² + 3x +1 by 5 + 2x we get remainder:
(a) 8/27
(b) 27/8
(c) – 27/8
(d) – 8/27

Question. If x – 2 is a factor of x³ – 3x +5a then the value of a is:
(a) 1
(b) –1
(c) 2/ 5
(d) -2 /5