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CBSE Guide Polynomials class 9 Notes
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9 Mathematics notes Chapter 2 Polynomials
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CBSE Class 09 Mathematics
CHAPTER – 2
- 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.
Classification of polynomials on the basis of number of terms
|No. of terms||Polynomial & Examples.|
|(i) 1||Monomial –|
|(ii) 2||Binomial – 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 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+
(iv) (x+a)(x+b)= +(a+b)x+ab
(viii) + + – 3xyz =(x+y+z) ( + + – xy – yz – zx)
++=3xyz if x+y+z=0
Polynomials class 9 Notes
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