NCERT Solutions for class 9 Maths Chapter 2 Exercise 2.4 Question 1

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A polynomial of degree 3 is called a cubic polynomial.

A polynomial of degree 2 is called a quadratic polynomial .

A polynomial of degree 1 is called a linear polynomial

Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials

respectively.

A polynomial of degree 3 is called a cubic polynomial.

A polynomial of degree 2 is called a quadratic polynomial .

A polynomial of degree 1 is called a linear polynomial

Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials

respectively.

geometrical representations of linear and quadratic polynomials and the geometrical

meaning of their zeroes.

Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.

The x occurring in a polynomial is commonly called either a variable or an indeterminate. When the polynomial is considered for itself, x is a fixed symbol which does not have any value its value is "indeterminate". It is thus more correct to call it an "indeterminate". However, when one considers the function defined by the polynomial, then x represents the argument of the function, and is therefore called a "variable". Many authors use these two words indifferently, but this may be sometimes confusing and is not done in this article.

That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms. Each term consists of the product of a number called the coefficient of the term2and a finite number of indeterminates, raised to nonnegative integer powers. The exponent on an indeterminate in a term is called the degree of that indeterminate in that term; the degree of the term is the sum of the degrees of the indeterminates in that term, and the degree of a polynomial is the largest degree of any one term with nonzero coefficient. Since x = x1, the degree of an indeterminate without a written exponent is one. A term and a polynomial with no indeterminates are called respectively a constant term and a constant polynomial 3 the degree of a constant term and of a nonzero constant polynomial is 0. The degree of the zero polynomial which has no term is not defined.

Polynomials of small degree have been given specific names. A polynomial of degree zero is a constant polynomial or simply a constant. Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. For higher degrees the specific names are not commonly used, although quartic polynomial for degree four and quintic polynomial for degree five are sometimes used. The names for the degrees may be applied to the polynomial or to its terms.

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