9th standard polynomials notes
Answers
The real numbers can also be expressed as polynomials. Like 3, 6, 7, are also polynomials without any variables. These are called constant polynomials. The constant polynomial 0 is called zero polynomial. The exponent of the polynomial should be a whole number. For example, x-2 + 5x + 2, cannot be considered as a polynomial, since the exponent of x is -2, which is not a whole number.
The highest power of the polynomial is called the degree of the polynomial. For example, in x3 + y3 + 3xy(x + y), the degree of the polynomial is 3. For a non zero constant polynomial, the degree is zero. Apart from these, there are other types of polynomials such as:
Linear polynomial – of degree one
Quadratic Polynomial- of degree two
Cubic Polynomial – of degree three
This topic has been widely discussed in class 9 and class 10.
Example of polynomials are:
20
x + y
7a + b + 8
w + x + y + z
x2 + x + 1
Answer:
Polynomial derived from the words “poly” which means “many” and the word “nomial” which means “term”. In maths, a polynomial expression consists of variables which are also known as indeterminates and coefficients. The coefficients involve the operations of subtraction, addition, non-negative integer exponents of variables and multiplication. A detailed polynomials Class 9 notes are provided here along with some important questions so that students can understand the concept easily.
Polynomials Class 9 Topics
The topics and subtopics covered in class 9 polynomials chapter 2 include:
Introduction
Polynomials in One Variable
Zeros of Polynomials
Remainder Theorem
Factorisation of Polynomials
Algebraic Identities
Polynomial Definition
Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. In the polynomial, each expression in it is called a term. Suppose x2 + 5x + 2 is polynomial, then the expressions x2, 5x, and 2 are the terms of the polynomial. Each term of the polynomial has a coefficient. For example, if 2x + 1 is the polynomial, then the coefficient of x is 2.
The real numbers can also be expressed as polynomials. Like 3, 6, 7, are also polynomials without any variables. These are called constant polynomials. The constant polynomial 0 is called zero polynomial. The exponent of the polynomial should be a whole number. For example, x-2 + 5x + 2, cannot be considered as a polynomial, since the exponent of x is -2, which is not a whole number.
The highest power of the polynomial is called the degree of the polynomial. For example, in x3 + y3 + 3xy(x + y), the degree of the polynomial is 3. For a non zero constant polynomial, the degree is zero. Apart from these, there are other types of polynomials such as:
Linear polynomial – of degree one
Quadratic Polynomial- of degree two
Cubic Polynomial – of degree three
This topic has been widely discussed in class 9 and class 10.
Example of polynomials are:
20
x + y
7a + b + 8
w + x + y + z
x2 + x + 1Polynomials in One Variable
Polynomials in one variable are the expressions which consist of only one type of variable in the entire expression.
Example of polynomials in one variable:
3a
2x2 + 5x + 15
Polynomial Class 9 Notes
To prepare for class 9 exams, students will require notes to study. These notes are of great help when they have to revise chapter 2 polynomials before the exam. The note here provides a brief of the chapter so that students find it easy to have a glance at once. The key points covered in the chapter have been noted. Go through the points and solve problems based on them.
Step-by-step explanation:
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