• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2022
    • RBSE Class 10th Board Model Papers 2022
    • RBSE Class 8th Board Model Papers 2022
    • RBSE Class 5th Board Model Papers 2022
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English First Flight & Footprints without Feet
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Class 9 Maths Notes Chapter 2 Polynomials

April 14, 2022 by Prasanna Leave a Comment

These comprehensive RBSE Class 9 Maths Notes Chapter 2 Polynomials will give a brief overview of all the concepts.

RBSE Class 9 Maths Chapter 2 Notes Polynomials

1. Unknown quantities in mathematical calculations are represented by symbols x, y, z, s, t The symbols a, b, c, etc. are used to denote constants. The branch of mathematics in which symbols, usually letters of the alphabets, representing numbers are combined according to the rules of arithmetic is known as algebra.

2. An algebraic expression is an expression that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply and divide).
For example- 2x + 3y + 15, 3x + 9, x ÷\(\frac{1}{x}\), x + y, y3 + z etc. are algebraic expressions.

RBSE Class 9 Maths Notes Chapter 2 Polynomials

3. If an algebraic expression contains only one variable x and exponents of variable x are whole numbers then such an expression is called a polynomial in one variable which is x and is denoted by the symbol f(x), p(x), q(x) A polynomial in one variable x of degree n is an expression of the form-
p(x) = anxn + an-1 xn-1 + …… + a2x2 + a1x + a0
a0, a1, a2,…., an are constants and an ≠ 0.
Also, a0, a1,a2,…., an are coefficients of x0, x, x2,…., xn respectively.
anxn, an-1n-1,…., a0 are known as terms of the polymial P(x). Also, ‘n’ is called degree of the polynomial, i.e., the highest power of variable in a polynomial is called the degree of polynomial.

4. Polynomials having only one term are called monomial.

5. Polynomials having two terms are called binomials.

RBSE Class 9 Maths Notes Chapter 2 Polynomials

6. Polynomials having three terms are called trinomials.

7. Polynomials having degree 1 are called linear polynomials.

8. Polynomials having degree 2 are called quadratic polynomials.

9. Polynomials having degree 3 are called cubic polynomials.

10. The constant polynomial 0 or p(x) = 0 is called the zero polynomial. The degree of a zero polynomial is not defined.

11. Real number ‘a’ is a zero (or root) of the polynomial p(x) if p(a) = 0. In this case, a is also called a root of the equation p(x) = 0.

RBSE Class 9 Maths Notes Chapter 2 Polynomials

12. Zeros of polynomial: Some results-

  • A zero of a polynomial need not be 0.
  • . 0 may be a zero of a polynomial.
  • Every linear polynomial has one and only one zero.
  • A polynomial can have more than one zero.

13. A linear polynomial in one variable has a unique root. A non-zero constant polynomial has no root. Every real number is a root of the zero polynomial.

14. Standard form of polynomial: The standard form of a polynomial is that form in which terms are written in the decreasing order of their power, e., write each term in order of degree, from highest to lowest, left to right.
For example- x6 – ax5 + x4 – ax3 + 3x – a + 2 is in standard form.

15. When two or more polynomials are written as product of two or more quantities, then each expression of the product is known as its factor. This process of getting factors is known as factorization.

RBSE Class 9 Maths Notes Chapter 2 Polynomials

16. Factorization of quadratic trinomial expressions : A polynomial of degree two and having three terms is known as a quadratic trinomial expression. Its standard form is ax2 + bx + c, where a, b, c are constants and a ≠ 0.

17. To factorize ax2 + bx + c, we write split the middle term bx as two terms such that when added, they give bx but, when multiplied they give the product of the first and the third term (i.e., product of ax2 and c).

18. Remainder theorem : Let p(x), be any polynomial of degree greater than or equal to one and let ‘a’ be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).

19. Factor theorem: If p(x) is a polynomial of degree n ≥ 1 and a is any real number, then
(i) x – a is a factor of p(x), if p(a) = 0 and
(ii) p(a) = 0, ifx – a is a factor of p(x).

RBSE Class 9 Maths Notes Chapter 2 Polynomials

20. Algebraic identities : An identity is an equality which is true for all values of the variables. Some important identities are :
(i) (x+y)2=x2+2xy+9
(ii) (x – y)2 = x2 – zxy + y2
(iii) x2-y2=(x + y)(x – y) .
(iv) (x+a)(x+b) = x2+(a+b)x + ab
(v) (x+y+z)2=x2+y2+z2+2xy+2yz+2zx
(vi) (x+y)3=x3+ y3+2xy(x+y)
(vii) (x  – y)3 = x3 – y3 – 3xy (x – y) = x3 -y3 – 3x2y + 3xy2
(viii) x3 +y3 + z3 – 3xyz = (x +y + z) (x2 +y2 + z2 – xy – yz – zx)

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)

Related

Filed Under: RBSE Notes

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Recent Posts

  • RBSE Solutions for Class 6 Maths Chapter 6 Decimal Numbers Additional Questions
  • RBSE Solutions for Class 11 Psychology in Hindi Medium & English Medium
  • RBSE Solutions for Class 11 Geography in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Hindi
  • RBSE Solutions for Class 3 English Let’s Learn English
  • RBSE Solutions for Class 3 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Maths in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 in Hindi Medium & English Medium
  • RBSE Solutions for Class 4 Hindi
  • RBSE Solutions for Class 4 English Let’s Learn English
  • RBSE Solutions for Class 4 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium

Footer

RBSE Solutions for Class 12
RBSE Solutions for Class 11
RBSE Solutions for Class 10
RBSE Solutions for Class 9
RBSE Solutions for Class 8
RBSE Solutions for Class 7
RBSE Solutions for Class 6
RBSE Solutions for Class 5
RBSE Solutions for Class 12 Maths
RBSE Solutions for Class 11 Maths
RBSE Solutions for Class 10 Maths
RBSE Solutions for Class 9 Maths
RBSE Solutions for Class 8 Maths
RBSE Solutions for Class 7 Maths
RBSE Solutions for Class 6 Maths
RBSE Solutions for Class 5 Maths
RBSE Class 11 Political Science Notes
RBSE Class 11 Geography Notes
RBSE Class 11 History Notes

Copyright © 2023 RBSE Solutions