Polynomials, Revision Notes: CBSE Class 9 MATH, Math

Polynomials

Polynomial

An algebraic expression in which the exponents of the variables are non-negative integers are called polynomials. For example, 3x⁴ + 2x³ + x + 9, 3x⁴etc are polynomials.

Constant polynomial: A constant polynomial is of the form $p (x) = k$ , where k is a real number. For example, –9, 10, 0 are constant polynomials.
Zero polynomial: A constant polynomial ‘0’ is called zero polynomial.

General form of a polynomial:

A polynomial of the form $p (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + ... + a_{1} x + a_{0},$ where $a_{0}, a_{1} ... a_{n}$ are constants and $a_{n} \neq 0$ .

Here, $a_{0}, a_{1} ... a_{n}$ are the respective coefficients of $x^{0}, x^{1}, x^{2}, ... x^{n}$ and n is the power of the variable x.

$a_{n} x^{n}, a_{n - 1} x^{n - 1} - a_{0}$ and $a_{0} \neq 0$ are called the terms of p(x).

Classification of polynomials on the basis of number of terms
- A polynomial having one term is called a monomial e.g. 3x, 25t^{3 etc.}
- A polynomial having two terms is called a binomial e.g. 2t – 6, 3x⁴ + 2x etc.
- A poly…

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