﻿ NCERT Solutions CBSE Class 10 Maths Chapter 2 | Polynomials

1. Introduction
2. Geometrical Meaning of the Zeroes of a Polynomial
3. Relationship between Zeroes and Coefficients of a Polynomial
4. Division Algorithm for Polynomials
5. Summary

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Chapter 2 - Polynomials

The easiest way to understand the chapter!

An expression containing variables, constant and any arithmetic operation is called polynomial. Polynomial comes from ‘poly’ means ‘many’ and ‘nominal’ means ‘terms,’ so we can also say “many terms.”

Polynomials are of three types:

·         Monomial = a polynomial which contains only one term, for example, = 3xy2

·         Binomial = a polynomial which contains two terms, for example, = 5x-1

·         Trinomial = a polynomial which contain three term for example = 3x2 + 5y-3

The ScoreXTM provides the best study material for CBSE Class 10 maths polynomial chapter to get the desired results.

What is the format of the course?

In the course of CBSE class 10 math chapter 2, we cover all the main topics given in the school book. Some are:-

1.         Some basic terms.

•           Degree of the polynomial: - The highest power of the variable in a polynomial is termed as the highest degree of the polynomial.

•           Constant polynomial: - A polynomial of degree zero is called constant polynomial.

•           Linear polynomial: - A polynomial of degree one E.g.:- 5x+1

•           Quadratic polynomial: - A polynomial of degree two E.g.:- 6x2-4x+1

•           Cubic polynomial: - A polynomial of degree three E.g.:- 3x3+6x2-4x-15

•           Bi-quadratic polynomial: - A polynomial of degree four E.g.:-24x4 +15x3 - 3x2 +x+1

2.         What is the Standard form?

The standard form for writing a polynomial put the terms with the highest degree first.

3.         What is Factor Theorem?

Let p(x) be a polynomial of degree n>1 and let ‘a’ be any real number. If p (a) =0 then (x-a) is a factor of p(x)

PROOF: - By the reminder theorem, p(x) = (x-a) q(x) + p (a)

1 if p (a) = 0 then p(x) = (x-a) q(x) which shows that x-a is a factor of p(x)

2 x-a is factor of p(x)

P(x) = (x-a) g(x) for same polynomial g(x)

So, p (a) = (a-a) g (a) =0

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1. Q.No 1 - Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?

1/3

1/8

2/8

1/16

1/10
2. Q.No 2 - Find the wrong number in the following series. 3252 , 3080 , 2958 , 2876 , 2826

3080

2876

2826

3252

None

2/10
3. Q.No 3 - 5, 50, 45, 450, 445, ?, 4445

4450

4600

4550

4500

None of the above

3/10
4. Q.No 4 - Find the wrong number in the following series. 1250, 1322 , 1452, 1674, 2024 , 2544

1250

1674

2544

2024

None of the above

4/10
5. Q.No 5 - The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is

30º

45º

60º

90º

None of the above

5/10
6. Q.No 6 - The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

0

1

10

19

None of the above

6/10
7. Q.No 7 - A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

12 days

15 days

16 days

18 days

None of the above

7/10
8. Q.No 8 - A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

650

690

698

700

None of the above

8/10
9. Q.No 9 - A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

10/21

11/21

2/7

5/7

None of the above

9/10
10. Q.No 10 - Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?

7

10

12

13

None of the above

10/10