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Learn polynomials in one variable, zeroes, remainder theorem, factorisation and algebraic identities with NCERT solutions for Class 9 Maths Chapter 2. Download PDF, access exercise-wise solutions and get ready for CBSE exams.
- Polynomials Class 9
CBSE Class 9 Maths Polynomials Notes:-Download PDF Here...
- Polynomials Class 9
- RT Solutions For Class 9 Maths Chapter 2 Polynomials Ex 2.2
- RT So1utions For C1ass 9 Maths Chapter 2 Polynomials Ex 2.3
- RT So1utions For Class 9 Maths Chapter 2 Polynomials Ex 2.4
- RT Solutions For Class 9 Maths Chapter 2 Polynomials Ex 2.5
Question 1. Find the value of the polynomial 5x – 4x2 + 3 at (i) x = 0 (ii) x = – 1 (iii) x = 2 Solution: 1et p(x) = 5x – 4x2 + 3 (i) p(0) = 5(0) – 4(0)2 + 3 = 0 – 0 + 3 = 3 Thus, the value of 5x – 4x2 + 3 at x = 0 is 3. (ii) p(-1) = 5(-1) – 4(-1)2 + 3 = – 5x – 4x2 + 3 = -9 + 3 = -6 Thus, the value of 5x – 4x2 + 3 at x = -1 is -6. (iii) p(2) = 5(2)...
Question 1. Find the remainder when x3 + 3x2 + 3x + 1 is divided by (i) x + 1 (ii) x – (iii) x (iv) x + π (v) 5 + 2x Solution: Let p(x) = x3 + 3x2 + 3x +1 (i) The zero of x + 1 is -1. ∴ p(-1) = (-1)3 + 3(-1)2 + 3(-1) +1 = -1 + 3- 3 + 1 = 0 Thus, the required remainder = 0 (ii) The zero of is Thus, the required remainder = (iii) The zero of x is 0. ...
Question 1. Determine which of the following polynomials has (x +1) a factor. (i) x3+x2+x +1 (ii) x4 + x3 + x2 + x + 1 (iii) x4 + 3x3 + 3x2 + x + 1 (iv) x3 – x2 – (2 +√2 )x + √2 Solution: The zero of x + 1 is -1. (i) Let p (x) = x3 + x2 + x + 1 ∴ p (-1) = (-1)3 + (-1)2 + (-1) + 1 . = -1 + 1 – 1 + 1 ⇒ p (- 1) = 0 So, (x+ 1) is a factor of x3 + x2+ x...
Question 1. Use suitable identities to find the following products (i) (x + 4)(x + 10) (ii) (x+8) (x -10) (iii) (3x + 4) (3x – 5) (iv) (y2+ ) (y2– ) (v) (3 – 2x) (3 + 2x) Solution: (i) We have, (x+ 4) (x + 10) Using identity, (x+ a) (x+ b) = x2 + (a + b) x+ ab. We have, (x + 4) (x + 10) = x2+(4 + 10) x + (4 x 10) = x2+ 14x+40 (ii) We have, (x+ 8) (...
constants. Similarly, quadratic polynomial in y will be of the form ay2 + by + c, provided a ≠ 0 and a, b, c are constants. We call a polynomial of degree three a cubic polynomial. Some examples of a cubic polynomial in x are 4x3, 2x3 + 1, 5x3 + x2, 6x3 – x, 6 – x3, 2x3 + 4x2 + 6x + 7. How many terms do you think a cubic polynomial in one ...
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- Term. In the polynomial, each expression is called a term. Suppose x2 + 5x + 2 is polynomial, then the expressions x2, 5x, and 2 are the terms of the polynomial.
- Coefficient. Each term of the polynomial has a coefficient. For example, if 2x + 1 is the polynomial, then the coefficient of x is 2.
- Types of Polynomial. A polynomial of 1 term is called a monomial. Example: 2x. A polynomial of 2 terms is called a binomial. Example: 5x + 2. A polynomial of 3 terms is called a trinomial.
- Constant Polynomial. Real numbers can also be expressed as polynomials. 3, 6, and 7 are also polynomials without any variables. These are called constant polynomials.
2 days ago · Learn about polynomials, their degrees, zeros, operations, and factor theorems with Vedantu's NCERT solutions for Class 9 Maths Chapter 2. Access exercise-wise solutions, PDF download, video links, and more resources for CBSE students.
- A polynomial in a variable x is an algebraic expression of the formp(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + . . . . .+ a₂x²+ a₁x + a₀ ,where a₀, a₁, a₂, . . . . .,...
- The remainder theorem states that if a polynomial p(x) is divided by (x - a), then the remainder is obtained by evaluating the expression p(a).Whil...
- An algebraic identity is an algebraic equation that is true for any values of the variables occurring in it.Algebraic identities are used to factor...
- Polynomials are algebraic expressions in which variables and constants terms are connected by various arithmetic operators. For ‘Polynomials in one...
- ‘Polynomials’ is one of the most important chapters in the Maths syllabus of class 9. The basic highlights of this chapter are listed below.Polynom...
- Remainder theorem, degree of polynomials, factorization, zeros of a polynomial, algebraic identities, etc., are explained in this chapter. These co...
- Vedantu’s NCERT solutions for Class 9 Maths Chapter 2 is presented in a very detailed and comprehensive manner. It includes all the concepts in an...
- No, it is easy to score high in your exams if you regularly practice with Vedantu’s NCERT solutions for Class 9 Maths Chapter 2. The solutions are...
- Polynomials are expressions that contain one or more terms with coefficients that are not zero. Polynomial terms can be variables, constants, or bo...
- When a polynomial p(x) is divided by the linear polynomial (x-a), then the remainder comes out to be p(a). The degree of the polynomial should be g...
Learn about polynomials in one variable, their degree, zeroes, factorisation and division. Find NCERT exercise questions and examples with solutions and videos at Teachoo.
Apr 30, 2024 · Find online and offline solutions for CBSE and UP Board exams based on NCERT books for class 9 maths chapter 2 polynomials. Learn the definitions, properties, types and examples of polynomials with videos and important terms.
