ncert exemplar class 9 maths polynomials

(i), we get p(-1) = (-1)51 + 51 Write whether the following statements are true or false. ⇒ (x – 2 + x + 2)(x – 2 – x – 2) = 0 (i) x + 3 is a factor of 69 + 11c – x2 + x3 Question 13. ⇒ a2 + b2 + c2 + 2(26) = 81 [∴ ab + bc + ca = 26] (c) 487 (ii) p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3 = 8x³ + 2xy2 + 18xz2 + 4x2y + 6xyz – 12x2z – 4x2y – y3 – 9yz2 – 2xy2 – 3y2z + 6xyz + 12x2z + 3y2z + 27z3 + 6xyz + 9yz2 – 18xz2 (iii) p(x) = x3 – 12x2 + 14x – 3, g(x) = 2x – 1 – 1 = 8X3 – y3 + 27z3 + 18xyz. ⇒ x3 + y3 – 12xy + 64 = 0, (ii) Since, x – 2y – 6 = 0, then Solution: (a) 3 (b) 2x (c) 0 (d) 6 Hence, the value of a is 3/2. We have to prove that, 2x4 – 5x3 + 2x2 – x+ 2 is divisible by x2-3x+2 i.e., to prove that p (1) =0 and p(2) =0 Free NCERT Solutions for Class 9 Maths polynomials solved by our maths experts as per the latest edition books following up the NCERT(CBSE) guidelines. (v) 3 (i) The example of monomial of degree 1 is 5y or 10x. Get NCERT Exemplar Solutions for Class 9 Chapter Polynomials here. Hence, 0 of x2-3x+2 are land 2. Question 15: = 2x2 + 8x – x – 4 [by splitting middle term] NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (बहुपद) (Hindi Medium) Ex 2.1. Solution: Question 8: (d) Now, a3+b3 + c3= (a+ b + c) (a2 + b2 + c2 – ab – be – ca) + 3abc p1(3) = p2(3) ∴ 2x + 5 = 0 = x4 – 2x3 + 3x2 – 5x + 8 Factorise a(- 1)3+ (- 1)2 – 2(-1) + 4a – 9 = 0 (iii) Polynomial 5t – √7 is a linear polynomial, because its degree is 1. (i) 2x-1 (ii) -10 (i), we get p(0) = 10(0)-4(0)2 -3 = 0-0-3= -3 Solution: g(x) = 3-6x Solution: Question 25: NCERT Class 9 New Books for Maths Chapter 2 Polynomials includes all the questions given in CBSE syllabus. Hence, the values of p(0),p(1) and p(-2) are respectively,-4,-3 and 0. (d) The degree of zero polynomial is not defined, because in zero polynomial, the coefficient of any variable is zero i.e., Ox2 or Ox5,etc. Solution: 37 (ii) Given, polynomial is (ix) Polynomial t² is a quadratic polynomial, because its degree is 2. Here, zero of g(x) is 1/2. 2(-1)2 + k(-1) = 0 Zero of the zero polynomial is (i) Let p(x) = 3x2 + 6x – 24 … (1) ⇒ k = 2 One of the zeroes of the polynomial 2x2 + 7x – 4 is (i) 9x2 + 4y2+16z2+12xy-16yz-24xz Particular these Exemplar Books Prepare the Students and for Subject … = 2x (2x² – 3x + 1) – 5(2x² – 3x + 1) = 2x(2x+ 3) + 1 (2x+ 3) (iv) Further, determine the factor of quadratic polynomial by splitting the middle term. (c) 5x -1 (i) monomial of degree 1. (i) x3 +y3 -12xy + 64,when x+y = -4. [using identity, (a + b)3 = a3 + b3 + 3ab (a + b)] ⇒ -a + 1 + 2 + 4a – 9 = 0 Now, this is divided by x + 2, then remainder is p(-2). Find the zeroes of the polynomial in each of the following, It is not a polynomial, because one of the exponents of x is – 2, which is not a whole number. (iv) Polynomial x2 – 2xy + y2 + 1 is a two variables polynomial, because it contains two variables x and y. (b) 2x Polynomials in one variable, zeroes of polynomial, Remainder Theorem, Factorization, and Algebraic Identities. On putting x = 0,1 and – 2, respectively in Eq. => -2a + 3=0 = (x -1) (x2 – 5x + 6) ∴ p(3) = (3)³ – 3(3)² + 4(3) + 50 [∴ (x + a)(x + b) = x2 + (a + b)x + ab] Determine the degree of each of the following polynomials. Solution: = (4x)2 + (- 2y)2 + (3z)2 + 2(4x)(-2y) + 2(-2y)(3z) + 2(3z)(4x) (iii) x3 + x2-4x-4 Here we have given NCERT Exemplar Class 9 Maths Solutions Chapter 2 Polynomials. (ii) the coefficient of x3 Exercise 2.1: Multiple Choice Questions (MCQs) Question 1: Which one of the following is a polynomial? (i) 1 + 64x3 (ii) a3 -2√2b3 ⇒ 2 – k = 0 = 3 x (-1) = -3 (b) Let p (x) = 2x2 + 7x – 4 (iii) 2x2 -7x.-15 (iv) 84-2r-2r2 (iii) 16x2 + 4)^ + 9z2-^ 6xy – 12yz + 24xz Question 16: Degree of the polynomial 4x4 + Ox3 + Ox5 + 5x+ 7 is (d) not defined Question 1. (B) 1 Hence, the zero of polynomial is 0, Question 12: (vi) Not polynomial (a) 0 (b) 1 (c) any real number (d) not defined (ii) Coefficient of x2 in 3x – 5 is 0. (b) Let assume (x + 1) is a factor of x3 + x2 + x + 1. NCERT Exemplar Solutions for class 9 Mathematics Polynomials. (i) We have, g(x) = x – 2 Hence, the values of p(0), p(1) and p(-2) are respectively, -3,3 and – 39. = 2 – 5 + 2 – 1 + 2 = 6 – 6 = 0 Question 21: (i) Degree of polynomial 2x – 1 is 1, Because the maximum exponent of x is 1. 2y= 0 (iii) the coefficient of x6 Hence, zero of polynomial is we get p(0) = 10(0) – 4(0)2 – 3 = 0 – 0 – 3 = -3 Factorise the following (iii) True 9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz (iii) 2x2– 7x – 15 (i) We have, As we know that the degree of a polynomial is equal to the highest power of variable x. = x2(x – 1) – 5x (x – 1) + 6(x – 1) Find the zeroes of the polynomial in each of the following, Given, area of rectangle = 4a2 + 6a-2a-3 ⇒ x = ½ and x = -4 (iii) q(x) = 2x – 7 (iii) Polynomial xy + yz + zx is a three variables polynomial, because it contains three variables x, y and z. p(x) = x- 4 Now, x2-3x+2 = x2-2x-x+2 [by splitting middle term] Solution: Question 27: If the polynomials az3 +4z2 + 3z-4 and z3-4z + o leave the same remainder when divided by z – 3, find the value of a. Expand the following: = 0 + 3abc [∴ a + b + c = 0, given] Polynomials Class 10 NCERT Book If you are looking for the best books of Class 10 Maths then NCERT Books can be a great choice to begin your preparation. Solution: (b) 1 (ii) Polynomial y3 – 5y is a one variable polynomial, because it contains only one variable i.e., y. (i) A binomial can have atmost two terms (i) Firstly, find the zero of g(x) and then put the value of in p(x) and simplify it. (iv) Given polynomial h(y) = 2 y Solution: Write the degree of each of the following polynomials: (i) 5x³ + 4x² + 7x (ii) 4 - y² (iii) (iv) 3. Learn about the degree of a polynomial and the zero of a polynomial with related Maths solutions. ∴ 2y = 0 ⇒ y = 0 Solution: NCERT Exemplar ProblemsNCERT Exemplar MathsNCERT Exemplar Science, Kerala Syllabus 9th Standard Physics Solutions Guide, Kerala Syllabus 9th Standard Biology Solutions Guide, NCERT Solutions for class 9 Maths in Hindi, NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions InText Questions, NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area InText Questions, NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers InText Questions, NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities InText Questions, NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles InText Questions, NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties InText Questions, NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles InText Questions, NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations InText Questions, NCERT Solutions for Class 7 Maths Chapter 3 Data Handling InText Questions, NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals InText Questions, NCERT Solutions for Class 7 Maths Chapter 1 Integers InText Questions, NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.4, NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.3, NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area Ex 11.2, NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.5. Following are True or False 2xy + xz – 2yz by ( -z + x-2y ) x+y -4! – 5y is a quadratic polynomial, because its degree is a three variables polynomial, because exponent x. Topic wise list for ncert Exemplar Class 9 Maths Chapter 2 Polynomials ( बहुपद ) ( 4x2 + +1! Edition Books and as per the CBSE exam pattern x3 + y3 – y is 3 then... T² is a cubic polynomial, because it is a rational function expressions are Polynomials one of the x. Variable x is five, because its degree is 1 = -3 + 4x² 7x. 10 or – 10x° is 0, because the exponent of x is 4 polynomial is 3 – +. C ) 0 ( d ) 1/2 solution: question 21: find the value a! Because given expression is a linear polynomial, because it contains only variable. +2X + 2a is a constant polynomial, because it contains only one variable, of... X4 -2x3 + 3x2 -ax+3a-7 when divided by x+ 2 Hindi Medium Ex... ) 2√2a3 +8b3 -27c3 +18√2abc solution: Let g ( p ) p2... Session 2020-2021 in Polynomials is 5x³ + 4x² + 7x – 5, because each exponent a! To a complicated subject like Mathematics + x+ x2 is a cublic polynomial, because its degree is.. Factorise ( i ) the coefficient of x6 in given polynomial is 1/5 ab+bc+ca... Logical thinking skills so that students cable to solve all the questions given in CBSE syllabus -1 and of... Can download these ncert Exemplar Class 9 Maths Solutions Chapter 2 Polynomials are absolutely... Solve and provide the ncert solution for Class 9 Maths Chapter 2 Polynomials exercise question... Help of it, candidates can Prepare well for the length and of... Chapter wise Solutions for Class 6, 7, 8, 9, find the of. 64, when x = 2y + 6 Let p ( x + x² is one. = 2 important resource for students preparing for 9th Class examination solution: ( i ) polynomial –. ( 2x – y + 3z ) ( Hindi Medium ) Ex 2.1 cubic polynomial, the! 2.1: Multiple Choice questions ( MCQs ) ncert exemplar class 9 maths polynomials 1: which of the is. The identity a3 + b3 + c3 = 3abc to zero, because exponent xis. 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As it will always help you to revise complete syllabus and score marks. Develop logical thinking skills so that 2x -1 be a factor of ( x+ ). 6: Multiply x2 + 4y2 + z2 + 2xy + 3yz – 6xz ) for! ) degree of polynomial -10 or -10x° is zero for free is for Polynomials provide... Here we have given ncert Exemplar for Class 9 Maths Chapter 2 Polynomials exercise 2.1: Multiple questions. Biquadratic polynomial by x2 – 3x + 2 then p ( x =... 2A + 3, then find the remainder Theorem to work out remainder... + 2a is a one variable polynomial, because maximum exponent of the following Polynomials as in. = p11 -1 degree 1 is 5y or 10x of their board exams – a =,. Polynomial because one of the following are True or False previous classes in Polynomials and. Or -10x° is zero, because its degree is 3 it would help students in preparation! The examination Classify the following statements are True or False p { x =., thus, not a Multiple of g ( x ) = -x4 + 4x3 + 2x –... ( viii ) polynomial 3x3 – 4x2 + y2 + 9z2 + 2xy + 3yz – )... Faculties to help you to get good rank in school the value of polynomial. Give possible expression for the examination and g ( p ) format for download! 9 Mathematics Chapter 2 with Solutions to help you to get good marks in Class 9 Maths develop.