Podcast
Questions and Answers
What is the degree of the polynomial 2x^3 + 5x^2 - 3x + 1?
What is the degree of the polynomial 2x^3 + 5x^2 - 3x + 1?
A polynomial can have a negative exponent.
A polynomial can have a negative exponent.
False
What is a zero of a polynomial?
What is a zero of a polynomial?
A value of the variable that makes the polynomial equal to zero.
To add or subtract polynomials, you need to combine ______________________ terms.
To add or subtract polynomials, you need to combine ______________________ terms.
Signup and view all the answers
Match the following types of polynomials with their definitions:
Match the following types of polynomials with their definitions:
Signup and view all the answers
The Remainder Theorem is used to find the zeroes of a polynomial.
The Remainder Theorem is used to find the zeroes of a polynomial.
Signup and view all the answers
What is a real number that cannot be expressed in the form p/q?
What is a real number that cannot be expressed in the form p/q?
Signup and view all the answers
The associative property of addition states that (a + b) + c = a + (b + c)
The associative property of addition states that (a + b) + c = a + (b + c)
Signup and view all the answers
What is the degree of the polynomial x^3 - 2x^2 + x - 1?
What is the degree of the polynomial x^3 - 2x^2 + x - 1?
Signup and view all the answers
A polynomial with three terms is called a ______________________.
A polynomial with three terms is called a ______________________.
Signup and view all the answers
What is the solution to the linear equation x - 2 = 3?
What is the solution to the linear equation x - 2 = 3?
Signup and view all the answers
The commutative property of multiplication states that a × b = b × a
The commutative property of multiplication states that a × b = b × a
Signup and view all the answers
Match the following types of polynomials with their definitions:
Match the following types of polynomials with their definitions:
Signup and view all the answers
What is the value of x that makes the equation 2x + 3 = 7 true?
What is the value of x that makes the equation 2x + 3 = 7 true?
Signup and view all the answers
What is an example of an irrational number?
What is an example of an irrational number?
Signup and view all the answers
The distributive property of multiplication over addition states that a × (b + c) = a × b + a × c
The distributive property of multiplication over addition states that a × (b + c) = a × b + a × c
Signup and view all the answers
Study Notes
Class 9 NCERT Maths Chapters 1 and 2: Polynomials
Chapter 1: Number Systems
Polynomials
- A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
- The variables are raised to non-negative integer powers.
Types of Polynomials
- Monomials: Polynomials with one term, e.g., 3x^2, 5y
- Binomials: Polynomials with two terms, e.g., x + 3, 2y - 4
- Trinomials: Polynomials with three terms, e.g., x^2 + 2x + 1
Degree of a Polynomial
- The degree of a polynomial is the highest power of the variable in the polynomial.
- For example, the degree of 3x^2 + 2x - 4 is 2.
Addition and Subtraction of Polynomials
- To add or subtract polynomials, combine like terms.
- Like terms are terms with the same variable(s) raised to the same power.
Chapter 2: Polynomials
Zeroes of a Polynomial
- A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.
- For example, if p(x) is a polynomial and p(a) = 0, then a is a zero of p(x).
Remainder Theorem
- If p(x) is a polynomial and p(a) = r, then (x - a) is a factor of p(x) - r.
- This theorem helps in finding the remainder when a polynomial is divided by a linear polynomial.
Factorisation of Polynomials
- Factorisation is the reverse process of multiplying polynomials.
- Factorisation helps in finding the zeroes of a polynomial.
Polynomials
- A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication, with variables raised to non-negative integer powers.
Types of Polynomials
- Monomials are polynomials with one term, such as 3x^2 or 5y.
- Binomials are polynomials with two terms, such as x + 3 or 2y - 4.
- Trinomials are polynomials with three terms, such as x^2 + 2x + 1.
Degree of a Polynomial
- The degree of a polynomial is the highest power of the variable in the polynomial.
- For example, the degree of 3x^2 + 2x - 4 is 2.
Operations on Polynomials
- To add or subtract polynomials, combine like terms, which are terms with the same variable(s) raised to the same power.
Zeroes of a Polynomial
- A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.
- For example, if p(x) is a polynomial and p(a) = 0, then a is a zero of p(x).
Remainder Theorem
- If p(x) is a polynomial and p(a) = r, then (x - a) is a factor of p(x) - r.
- This theorem helps in finding the remainder when a polynomial is divided by a linear polynomial.
Factorisation of Polynomials
- Factorisation is the reverse process of multiplying polynomials.
- Factorisation helps in finding the zeroes of a polynomial.
Number Systems
- Real numbers can be represented on the number line and include both rational and irrational numbers.
Rational Numbers
- Rational numbers can be expressed in the form p/q, where p and q are integers and q ≠ 0.
- Examples of rational numbers include 3/4 and 22/7.
Irrational Numbers
- Irrational numbers cannot be expressed in the form p/q.
- Examples of irrational numbers include π, √2, and e.
Properties of Real Numbers
- The commutative property of real numbers states that a + b = b + a and a × b = b × a.
- The associative property of real numbers states that (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).
- The distributive property of real numbers states that a + (b + c) = a + b + a + c and a × (b + c) = a × b + a × c.
Polynomials
Introduction to Polynomials
- A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
- Examples of polynomials include 2x^2 + 3x - 4 and x^4 - 3x^2 + 2.
Types of Polynomials
- Monomials are polynomials with one term, such as 2x^2.
- Binomials are polynomials with two terms, such as x^2 + 3x.
- Trinomials are polynomials with three terms, such as x^2 + 2x + 1.
Degree of a Polynomial
- The degree of a polynomial is the highest power of the variable in the polynomial.
- The degree of 2x^2 + 3x - 4 is 2.
Zeroes of a Polynomial
- A zero of a polynomial is a value of the variable that makes the polynomial equal to zero.
- The zeroes of x^2 + 2x + 1 are -1 and -1.
Linear Equations
Introduction to Linear Equations
- A linear equation is an equation in which the highest power of the variable is 1.
- Examples of linear equations include 2x + 3 = 7 and x - 2 = 3.
Solution of Linear Equations
- Linear equations can be solved by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
- To solve 2x + 3 = 7, first subtract 3 from both sides to get 2x = 4, then divide both sides by 2 to get x = 2.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of polynomials, including their definition, types, and properties, as covered in Class 9 NCERT Maths Chapters 1 and 2.
