CBSE Class 10 Maths Chapter 2 Polynomials Objective Questions

CBSE Class 10 Maths Chapter 2 Polynomials Objective Questions cover all the important concepts present in the chapter. It explains Polynomials and their applications in detail in this chapter. Students can learn about the division algorithm for polynomials of integers and also whether the zeros of quadratic polynomials are related to their coefficients from this chapter. As this is one of the important topics in Maths, it comes under the unit – Algebra. This CBSE Class 10 Maths Chapter 2 – Polynomials Objective Questions help students to get acquainted with solving MCQs.

Here, for the convenience of the students, we have compiled a list of topic-wise MCQs from this chapter. From the upcoming academic session, objective-type questions are expected to appear more often.

List of Sub-Topics Covered in Chapter 2

Solving these CBSE Class 10 Maths Objective Questions will help the students to get a proper foundation in the subject. These MCQs are compiled in this article for students to download and practise so that they get acquainted with answering the objective type of questions. Meanwhile, see here the list of sub-topics we have covered in this chapter:

2.1 Basics Revisited (2 MCQs from This Topic)

2.2 Graphical Representations (2 MCQs Covered from This Topic)

2.3 Visualisation of a Polynomial (2 MCQs from This Topic)

2.4 Zeros of a Polynomial (3 MCQs from This Topic)

2.5 Factorisation of polynomials (3 MCQs from This Topic)

2.6 Relationship between Zeros and Coefficient (2 MCQs from The Topic)

2.7 Division Algorithm (2 MCQs Covered from This Topic)

2.8 Algebraic Identities (3 MCQs from This Topic)

Download Free CBSE Class 10 Maths Chapter 2 – Polynomials Objective Questions PDF

Basics Revisited

1. 1. Write the coefficient of  x² in each of the following.

Answer: C. 1, -1, π/2, 0

Solution: The constant multiplied by x² is the coefficient of x²

(1) 2 + x² + x → coefficient of x² = 1

(2) 2 – x² + x³ → coefficient of x² = -1

(3) (π/2) x² +x → coefficient of x² = π/2

(4) √2 x−1 → coefficient of x² = 0

2. 2. The polynomial p(x) = x−323 is a ___.
      1. Constant Polynomial
      2. Cubic Polynomial
      3. Quadratic Polynomial
      4. Linear Polynomial

Answer: D. Linear Polynomial

Solution: The polynomial of degree one is called a linear polynomial.

Therefore, x−323 is a linear polynomial.

Graphical Representations

3. 3. Three curves, i.e. a) y = x²b) y = x⁴c) y = x^6, are depicted in the graph shown below. Which of the polynomials does graph 3 represent?

3. 3. 1. y = x⁴
      2. y = x⁶
      3. y = x²
      4. Cannot be determined

Answer: B. y = x⁶

Solution: Consider the polynomial where n is a positive even integer.

As the value of n increases, then the curve goes closer to the positive y-axis.

Thus, graph 3 represents the polynomial x⁶

4. 4. Three curves, i.e.,

a) Y = −x²

b) y = −x³

c) y = −x⁷

are depicted in the following graph and are numbered from 1 to 3.

Identify the correct relation.

4. 4. 1. (a)-(1) , (b)-(2), (c)-(3)
      2. (a)-(3) , (b)-(2), (c)-(1)
      3. (a)-(1) , (b)-(3), (c)-(2)
      4. (a)-(2) , (b)-(3), (c)-(1)

Answer: A. (a)-(1), (b)-(2), (c)-(3)

Solutions: When a polynomial is of the form y = −xⁿ, the graph of the polynomial is the mirror image of the graph of the polynomial y = xⁿ.

Also, when the value of n increases, the graph draws closer to the y-axis.

Thus, graph 1 represents y = −x², graph 2 represents y = −x³ and graph 3 represents y = −x⁷

Visualisation of a Polynomial

5. 5. If x = 2,y = −1, then the value of x²+4xy+4y² is
      1. 2
      2. -1
      3. 1
      4. 0

Answer: D. 0

Solution: Substituting the values,

X²+4xy+4y²

= (2)² + 4(2) (-1) + 4(-1)²

= 4−8+4=0

6. 6. According to the graph below, the product of the zeroes of the polynomial will be

6. 6. 1. Cannot be determined
      2. Zero
      3. Negative
      4. Positive

Answer: C. Negative

Solution: One of the zeros of the polynomial lies on the positive x-axis. Thus, the abscissa or the x -coordinate, which is the corresponding zero, is positive.

The other zero lies on the negative x-axis. Thus, the abscissa or x -coordinate, which is the corresponding zero, is negative.

Thus, the product of zeroes is going to be positive negative = negative.

Zeroes of a Polynomial

7. 7. The number of polynomials having 3 and 7 as zeroes are
      1. More than 3
      2. 3
      3. 2
      4. 1

Answer: A. More than 3

Solution: (x-3)^A(X-7)^B, where a and b can take any natural number values.

Hence, infinite possibilities.

8. 8. If α, β and γ are the zeros of the polynomial

8. 8. 1. – (b/a)
      2. – (c/d)
      3. a/d
      4. c/d

Answer: B. –(c/d)

Solutions: If α, β and γ are the zeros of the polynomial

9. 9. If α, β are the zeros of the polynomial, x²-px +36 and α² + β² = 9, then what is the value of p?
      1. 6
      2. 3
      3. 9
      4. 8

Answer: C. 9

Solution: Here a = 1, b = -p, c = 36.

Factorisation of Polynomials

10. 10. What is the factorisation of 2x²−7x−15?
        1. (x+5) (2x-3)
        2. (x+3) (2x-5)
        3. (x-5) (2x+3)
        4. (x-3) (2x-5)

Answer: C. (x-5) (2x+3)

Solution: Find two numbers such that their product is -30 and the sum is -7.

11. 11. What is the factorisation of x² −5x+6?
        1. (x+5) (x-3)
        2. (x-6) (x+1)
        3. (x-1) (x+5)
        4. (x-2) (x-3)

Answer: D. (x-2) (x-3)

12. 12. Which among the following options is one of the factors of x²+ x/6+ 1/6?
        1. 3x +1
        2. 2x + 1
        3. X – (1/5)
        4. X- (1/2)

Answer: B. 2x +1

Relationship between Zeroes and Coefficients

13. 13. Find the sum  and product of roots  for the given polynomial:

Answer: A. -(1/2), – (5/2)

Solution: We know that, for a quadratic equation

ax² + bx+ c = 0 sum of roots = α+β & product of roots = αβ

Comparing 2x²+x−5=0 with ax² + bx+ c=0, we get

a=2, b=1, c=−5

⇒α+β= – (1/2)

⇒αβ= – (5/2)

14. 14. If p, q & r are the zeroes of a cubic polynomial ax³+bx²+cx+d, then what will be p+q+r?
        1. c/a
        2. b/a
        3. –(c/a)
        4. –(b/a)

Answer: D. –(b/a)

Solution: We know that for a cubic polynomial ax³+bx²+cx+d Sum of zeroes = –(b/a)

Therefore, p+q+r= – (b/a).

Division Algorithm

15. 15. In the division algorithm, when should one stop the division process?

1. When the remainder is zero.

2. When the degree of the remainder is less than the degree of the divisor.

3. When the degree of the quotient is less than the degree of the divisor.

15. 15. 1. Statements 1 and 2 are correct
        2. Statements 2 and 3 are correct
        3. Statements 1 and 3 are correct
        4. Only statement 3 is correct

Answer: (A) Statements 1 and 2 are correct

Solution: We stop the division process when either the remainder is zero, or its degree is less than the degree of the divisor.

16. 16. If the remainder when x³+2x²+kx+3 is divided by x-3 is 21, find the zeroes of x³+2x²+kx−18.
        1. -2, 3, 3
        2. -3, 2, 3
        3. -3, -2,3
        4. -3,-3, 2

Answer: C. -3, -2, 3

Solution: P (3) = 48 + 3k = 21

⇒ K = -9

Hence, x³+2x²−9x+3= (x−3) x Quotient + 21

⇒x³+2x²−9x−18 =9x−3) x Quotient

Quotient = (x3+2x²−9x−18) / (x-3)

Factorising the quotient, x²+ 5x +6= x²+ 3x + 2x +6 = x(x+3) +2(x+3) =(x+2) (x+3)

Hence, the factors of x³+2x²−9x−18 are x−3, x+2 and x+3

⇒ the zeroes are -3,-2, 3.

Algebraic Identities

17. 17. If x+x^-1 = 10, (x≠0), then what will be x²+x^-2?
        1. 100
        2. 10
        3. 98
        4. 102

Answer: C. 98

18. 18. f α and β are the zeros of the polynomial

18. 18. 1. –(45/8)
        2. 45/8
        3. -(8)/ 45
        4. 8/45

Answer: B. 45/8

19. 19. What term should be added to a²+2ab to make it a perfect square?
        1. 2ab
        2. a²
        3. b²

Answer: C. b²

Solution: To make (a²+2ab) a perfect square, b² is to be added.

So (a²+2ab+b²) will become a perfect square using the identity

Here, we have compiled 19 questions from Chapter 2 Polynomials of the CBSE Class 10 Maths in the downloadable PDF link that we have given in the article above. Also, find some extra CBSE Class 10 Maths Chapter 2 MCQs here.

CBSE Class 10 Maths Chapter 2 Extra MCQs

1. Given that one zero of the quadratic polynomial x² + 3x + k is 2,  what is the value of k? 
(a) -10
(b) 10
(c) 5
(d) -5

2. Given that the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and -3, what are a and b?
(a) a = 5, b = -1
(b) a = -7, b = -1
(c) a = 2, b = -6
(d) a – 0, b = -6

3. The number of zeroes that a linear polynomial has/have is _____.
(a) 1
(b) 2
(c) 0
(d) 3

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