 # CBSE Class 10 Maths Chapter 2-Polynomials Objective Questions

Polynomials is the second chapter for CBSE Class 10 Maths. It discusses the Polynomials and its 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 its coefficients from this chapter. As this is one of the important topics in Maths, it comes under the unit – Algebra.

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

### List of Sub-Topics Covered In This Chapter

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 the article for students to download and practice 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 Visualization of a Polynomial (2 MCQs From This Topic)

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

2.5 Factorization of polynomials (3 MCQs Asked 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 Covered)

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

### Basics Revisited

1. Write the coefficient of  x2 in each of the following?  Solution: The constant multiplied to 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 X= π/2

(4) √2 x−1 → coefficient of X2 = 0

1. The polynomial p(x)=x−323 is a___
1. Constant Polynomial
2. Cubic Polynomial
4. Linear Polynomial

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

Therefore, x−323 is a linear polynomial

### Graphical Representations

1. Three curves i.e.

a) y=x2

b) y=x4

c) y=x6

are depicted in the graph shown below. Which of the polynomials does the graph 3 represent? 1. y=x4
2. y=x6
3. y=x2
4. Cannot be determined

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, the graph 3 represents the polynomial x6

1. 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. 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)

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

### Visualization of a polynomial

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

Solution: Substituting the values,

X2+4xy+4y2

= (2)2 + 4(2) (-1) + 4(-1)2

= 4−8+4=0

1. According to the graph below, the product of the zeroes of the polynomial will be 1. Cannot be determined
2. Zero
3. Negative
4. Positive

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

1. Number of polynomials having 3 and 7 as zeroes are?
1. More than 3
2. 3
3. 2
4. 1

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

Hence infinite possibilities

1. If α,β and γ are the zeros of the polynomial 1. – (b/a)
2. – (c/d)
3. a/d
4. c/d

Solutions: If α, β and γ are the zeros of the polynomial 1. 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

Solution: Here a = 1, b = -p, c = 36. ### Factorization of polynomials

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

Solution: Find two numbers such that their product is -30 and sum is -7. 1. What is the factorization of x2 −5x+6?
1. (x+5) (x-3)
2. (x-6) (x+1)
3. (x-1) (x+5)
4. (x-2) (x-3) 1. Which among the 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) ### Relationship between zeroes and coefficient

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

a=2, b=1, c=−5

⇒α+β= – (1/2)

⇒αβ= – (5/2)

1. 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)

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

1. In 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.

1. Statement 1, 2 are correct
2. Statement 2, 3 are correct
3. Statement 3, 1 are correct
4. Only 3 is correct

Answer: (A)Statement 1, 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.

1. 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

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) Factorizing 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

1. If x+x-1=10, (x≠0) then evaluate :

x2+ x-2

1. 100
2. 10
3. 98
4. 102 1. f α and β are the zeros of polynomial 1. –(45/8)
2. 45/8
3. -(8)/ 45
4. 8/45 1. What term should be added to a2+2ab to make it a perfect square?
1. 2ab
2. a2
3. b2 