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## CBSE Guide Polynomials class 9 Notes

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## 9 Mathematics notes Chapter 2 Polynomials

Download CBSE class 9th revision notes for Chapter 2 Polynomials in PDF format for free. Download revision notes for Polynomials class 9 Notes and score high in exams. These are the Polynomials class 9 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

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**CBSE Class 09 Mathematics Revision Notes CHAPTER – 2 POLYNOMIALS**

- Polynomials in one Variable
- Zeroes of a Polynomial
- Remainder Theorem
- Factorisation of Polynomials
- Algebraic Identities

**Constants** : A symbol having a fixed numerical value is called a constant.

**Variables **: A symbol which may be assigned different numerical values is known as variable.

**Algebraic expressions** : A combination of constants and variables connected by some or all of the operations +, -, *,/ is known as algebraic expression.

**Terms :** The several parts of an algebraic expression separated by ‘+’ or ‘-‘ operations are called the terms of the expression.

**Polynomials **: An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial.

(i)

is a polynomial in variable x.(ii)

is an expression but not a polynomial.Polynomials are denoted by p(x), q(x) and r(x) etc.

**Coefficients **: In the polynomial , coefficient of respectively and we also say that +1 is the constant term in it.

Degree of a polynomial in one variable: In case of a polynomial in one variable the highest power of the variable is called the degree of the polynomial.

A polynomial of degree n has n roots.

Classification of polynomials on the basis of degree.

degree | Polynomial | Example |

(a) 1 | Linear | |

(b) 2 | Quadratic | |

(c) 3 | Cubic | |

(d) 4 | Biquadratic |

Classification of polynomials on the basis of number of terms

No. of terms | Polynomial & Examples. |

(i) 1 | Monomial – |

(ii) 2 | Binomial – | etc.

(iii) 3 | Trinomial- |

**Constant polynomial** : A polynomial containing one term only, consisting a constant term is called a constant polynomial.The degree of non-zero constant polynomial is zero.

**Zero polynomial** : A polynomial consisting of one term, namely zero only is called a zero polynomial.

The degree of zero polynomial is not defined.

**Zeroes of a polynomial** : Let be a polynomial. If =0, then we say that “a” is a zero of the polynomial of p(x).

**Remark :** Finding the zeroes of polynomial p(x) means solving the equation p(x)=0.

**Remainder theorem :** Let be a polynomial of degree and let a be any real number. When f(x) is divided by then the remainder is f ( a)

**Factor theorem :** Let f(x) be a polynomial of degree n > 1 and let a be any real number.

If f(a) = 0 then, (x – a) is factor of f(x)

If f(x – a) is factor of f(x) then f(a) = 0

**Factor :** A polynomial is called factor of divides exactly.

**Factorization** : To express a given polynomial as the product of polynomials each of

degree less than that of the given polynomial such that no such a factor has a factor of

lower degree, is called factorization.

**Some algebraic identities useful in factorization:**

(i)

= +2xy+(ii)

= -2xy+(iii)

– =(x-y)(x+y)(iv) (x+a)(x+b)=

+(a+b)x+ab(v)

= +2xy+2yz+2zx(vi)

= + +3xy(x+y)(vii)

= – -3xy(x-y)(viii)

+ + – 3xyz =(x+y+z) ( + + – xy – yz – zx)+ + =3xyz if x+y+z=0

(ix)

(x)

## Polynomials class 9 Notes

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**CBSE Class-9 Revision Notes and Key Points**

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