Please refer to Polynomials Class 9 Mathematics Notes and important questions below. The Class 9 Mathematics Chapter wise notes have been prepared based on the latest syllabus issued for the current academic year by CBSE. Students should revise these notes and go through important Class 9 Mathematics examination questions given below to obtain better marks in exams
Polynomials Class 9 Mathematics Notes and Questions
The below Class 9 Polynomials notes have been designed by expert Mathematics teachers. These will help you a lot to understand all the important topics given in your NCERT Class 9 Mathematics textbook.
Refer to Chapter 2 Polynomials Notes below which have been designed as per the latest syllabus issued by CBSE and will be very useful for upcoming examinations to help clear your concepts and get better marks in examinations.
1. Polynomials in one Variable
2. Zeroes of a Polynomial
3. Remainder Theorem
4. Factorisation of Polynomials
5. 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 +, -, X and 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 nonnegative integral powers is called a polynomial.
(i) 5x2 – 4x2 – 6x – 3 is a polynomial in variable x.
(ii) (ii) 5 + 8x3/2 + 4x-2 is an expression but not a polynomial.
Polynomials are denoted by p(x), q(x) and r(x)etc.
• Coefficients: In the polynomial x3 + 3x2 + 3x +1, coefficient of x3, x2 , x are1, 3, 3 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.
• Classification of polynomials on the basis of degree.
Degree Polynomial Example
(a) 1 Linear x +1, 2x + 3etc.
(b) 2 Quadratic ax2 + bx + c etc.
(c) 3 Cubic x3 + 3x2 +1 etc. etc.
(d) 4 Biquadratic x4 -1
Classification of polynomials on the basis of no. of terms
No. of terms Polynomial & Examples.
(i) 1 Monomial -5,3x1/3, y etc.
(ii) 2 Binomial – (3+ 6x), (x – 5y) etc.
(iii) 3 Trinomial – 2x2 + 4x + 2 etc. etc.
• 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 p(x) be a polynomial. If p(a) =0, then we say that 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 f (x) be a polynomial of degree n ³ 1 and let a be any real number. When f(x) is divided by (x – a) 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.
(i) If f (a) = 0 then (x – a) is factor of f (x)
(ii) If (x – a) is factor of f (x)then f (a) = 0
• Factor: A polynomial p(x) is called factor of q(x) divides q(x) 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.