(d)-2 Show that, Solution: It depends upon the degree of the polynomial (i) We have, g(x) = x – 2 Hence, one of the factor of given polynomial is 10x. (c) 5x -1 (ii) p(y) = (y + 2)(y – 2) NCERT Exemplar for Class 9 Maths Chapter 2 With Solution | Polynomials. Question 1. (a) 2             (b) 0           (c) 1          (d)½ If p (x) = x + 3, then p(x)+ p (- x) is equal to Justify your answer: (vi) Not polynomial If both x – 2 and x -(1/2)  are factors of px2+ 5x+r, then show that p = r. (ii) p(x) = 2x3 – 11x2 – 4x+ 5,  g(x) = 2x + l. Thinking Process Expand the following: Hence, zero of the polynomial p(x) is -5/2. (b) 2x Solution: Question 35: (ii) p(x) = x3 -3x2 + 4x + 50, g(x)= x – 3 On putting p=1 in Eq. = 27a3 – 54a2b + 36ab2 – 8b3. 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 Let p(x) = x3 – 2mx2 + 16 a = 3/2. (i) We have, 1033 = (100 + 3)3 Put y² + y – 6 = 0 ⇒ y² + 3y – 2y – 6 = 0 = 4x3 + 2x + 2 which is not a polynomial of degree 4. = 10-4-3= 10-7= 3 (ii) Polynomial y3 – 5y is a one variable polynomial, because it contains only one variable i.e., y. Fi nd (2x – y + 3z) (4x2 + y2 + 9z2 + 2xy + 3yz – 6xz). (ii) a3 – 2√2b3 (i), we get Solution: ⇒ a2 + b2 + c2 = 25 – 20 Because exponent of the variable x is 1/2, which is not a whole number. NCERT Mathematics Exemplar Chapter Unit 2 Polynomials Class 9 Books PDF SelfStudys is a No.1 Educational Portal in India who Provides You Free NCERT Mathematics Exemplar Chapter Unit 2 Polynomials Books with Solutions in PDF format for 6 to 12 Solved by Subject Expert as per NCERT … a3 + b3 + c3 – 3 abc = (a + b + c)(a2 + b2 + c2 -ab-bc-ca) (a) 3               (b) 2x            (c) 0                   (d) 6 Solution: ⇒ x3 + y3 + 64 = 12xy Hence, x – 2 is a factor of p(x). Question 19. (iv) The constant term in given polynomial is 1/5. (iii) Given, polynomial is q(x) = 2x -7 For zero of polynomial, put q(x) =  2x-7 = 0 (iii) The coefficient of x6 in given polynomial is -1. Therefore, remainder is 0. (i) Polynomial 2 – x² + x³ is a cubic polynomial, because its degree is 3. (i), we get (i) p(x)= x – 4 (c) xy2 (vii) Polynomial y³ – y is a cubic polynomial, because its degree is 3. (c) x4 + x3 + x2 +1      (d) x4 + 3x3 + 3x2 + x +1 Zero of the polynomial p(x)=2x+5 is NCERT Exemplar Class 9 Maths Solutions Polynomials. (ii) True = 8 – 20 + 8 – 3 = – 7 (iii) xy+ yz +zx     (iv) x2 – Zxy + y2 +1 (i) We have, (v) -3 is a zero of y2 + y – 6 (b) 3x2 + 5 [polynomial and also a binomial] Solution: (iv) False = (x – 1) (x + 1)(3x -1), Question 25. (i) Since, x + y + 4 = 0, then Question 18. = 2x(2x + 3) + 1 (2x + 3) Let g (p) = p10 -1  …(1) (c) 1 (i) monomial of degree 1. Give possible expression for the length and breadth of the rectangle whose area is given by 4a2 +4a – 3. Find the zeroes of the polynomial p(x) = (x – 2)2 – (x + 2)2. Solution: Question 36: (iv) True (iii) trinomial of degree 2. Hence, √2 is a polynomial of degree 0, because exponent of x is 0. (c) 2 With the help of the NCERT Exemplar Class 9 Maths, candidates can understand the level and type of questions that are asked in the exam. (iv) x2 – Zxy + y2 + 1 Hence, zero of polynomial is X For zero of polynomial, put h(y) = 0 (a) 0        (b) 1           (c) any real number               (d) not defined (i) 2x – 1 = (x – 1) (x2 – 3x – 2x + 6) (ix) Polynomial t2 is a quadratic polynomial, because maximum exponent of t is 2. = x2 (x4 + x2 + 1) – 1(x4 + x2 + 1) Determine which of the following polynomial has x – 2 a factor Put 3x + 1 = 0 ⇒ x = -1/3 ⇒ a2 + b2 + c2 + 2 (ab + bc + ca) = 81 (a) 0                 (b) 1                   (c) 4√2              (d) 8 √2 +1 (a) 3 Factorise Factorise the following: (c) 0 Now, p1(3) = a(3)3 + 4(3)2 + 3(3) – 4 (iv) 0 and 2 are the zeroes of t2 – 2t Get NCERT Exemplar Solutions for Class 9 Chapter Polynomials here. Zero of the zero polynomial is (d) 50 (i) False = 4x³ – 6x² + 2x – 10x² + 15x – 5 (d) Now, (25x2 -1) + (1 + 5x)2 Expand the following NCERT Class 9 Maths Exemplar book has 14 chapters on topics like Rational Numbers, Coordinate Geometry, Triangles, Heron’s formula, Statistics, and Probability. = x3 + 27 + 9x2 + 27x Hence, the coefficient of x in (x + 3)3 is 27. (i), we get p(0) =(0+2)(0-2)= -4 Let p1(z) = az3 + 4z2 + 3z – 4 and p2(z) = z3 – 4z + o (i) Polynomial and h(p) = p11 -1. Factorise Solution: We know that, NCERT Exemplar Class 9 for Maths Chapter 2 – Polynomials. (iii) Degree of polynomial x3 – 9x + 3x5 is 5, because the maximum exponent of x is 5. = (x – 2)(x + 3)(2x – 5), (ii)We have, x3 – 6x2 + 11x – 6 = 4x³ – 16x² + 17x – 5 (i) Given, polynomial is e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, putx-k = 0=>x = k Hence, zero of the zero polynomial be any real number. = 1000027 + 92700 = 1092727, (ii) We have, 101 × 102 = (100 + 1) (100 + 2) Hindi Mathematics. (c) -1 p(-1)=0 polynomial is divided by the second polynomial x4 + 1 and x-1. 2a =3 Solution: Question 30: ⇒ x3 – 8y3 – 216 = 36xy (a) 0 = 4a2 + 4a – 3 [by splitting middle term] One of the factors of (25x2 – 1) + (1 + 5x)2 is (i) A Binomial can have atmost two terms. Solution: (i) Polynomial 2 – x2 + x3 is a cubic polynomial, because maximum exponent of x is 3. 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. Substituting x = 2 in (2), we get (ii) Given, polynomial is Prove that (a +b +c)3 -a3 -b3 – c3 =3(a +b)(b +c)(c +a). NCERT 9 Mathematics Exemplar Problem Text book Solutions. (i) Firstly, determine the factor by using splitting method. By remainder theorem, find the remainder when p(x) is divided by g(x) Question 15. (i) Firstly, find the zero of g(x) and then put the value of in p(x) and simplify it. (iv) Further, determine the factor of quadratic polynomial by splitting the middle term. (x) Polynomial √2x – 1 is a linear polynomial, because its degree is 1. Solution: Solution: Question 27: = -1 – 2 + 4 – 1 = 0 Hence, one of the factor of given polynomial is 3xy. Question 15. = 27a+ 36+ 9-4= 27a+ 41 x³ + (-2y)3 + (-6)3 = 3x(-2y)(-6) (ii) 2x – 3 is a factor of x + 2x3 -9x2 +12 if a + b+c = Q, now use the identity a3 + b3 + c3 = 3abc. Now, x2-3x + 2 = x2 – 2x – x + 2 (ix) Polynomial t² is a quadratic polynomial, because its degree is 2. (ii) g(x)= 3 – 6x Check whether p(x) is a multiple of g(x) or not Hence, x – 2 is not a factor of p(x). 2x4 – Sx3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. Solution: (i) Polynomial x2 + x + 1 is a one variable polynomial, because it contains only one variable i.e., x. (d) (2x – 1) (2x – 3) (i) 1 + 64x3          (ii) a3 -2√2b3 Hence, the value of k is 2. (i) p(x) = 10x – 4x2 – 3 (ii) p(y) = (y + 2)(y – 2) L.H.S. (d) -2 (iv) Degree of polynomial y3(1-y4) or y3 – y7 is seven, because the maximum exponent of y is seven. Solution: (i), we get p(-1) = (-1)51 + 51 (iii) Degree of polynomial x3 – 9x + 3xs is five, because the maximum exponent of x is five. Question 20: Given, area of rectangle = 4a2 + 6a-2a-3 = 2x2 + 8x – x – 4 [by splitting middle term] Since, x + 2a is a factor of p(x), then put p(-2a) = 0 (-2a)5 – 4a2 (-2a)3 + 2(-2a) + 2a + 3 = 0 => -32a5 + 32a5 -4a + 2a+ 3 = 0 = 4a2 + 6a – 2a – 3 Factorise: NCERT Solutions for Class 9 Maths Chapter 2 Polynomials (बहुपद) (Hindi Medium) Ex 2.1. For zeroes of polynomial, put p(x) = 0 = -2[r(r + 7) -6(r + 7)] Because a binomial is a polynomial whose degree is a whole number which is greater than or equal to one. Therefore, we can not exactly determine the highest power of variable, hence cannot define the degree of zero polynomial. NCERT Exemplar Class 9 for Maths Chapter 3 – Coordinate Geometry (i) We have, (3a – 2b)3 Because the sum of any two polynomials of same degree has not always same degree. (i) a3 -8b3 -64c3 -2Aabc Download for free (or view) PDF file NCERT Class 9 Mathematics Exemplar Problems (Important for UPSC-CSE, CA, UGC-NET) for UPSC-CSE, CA, UGC-NET. (iii) Polynomial 5t -√7 is a linear polynomial, because maximum exponent of t is 1. 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. Hence, quotient = x³ + x² + x + 1 and remainder = 2. Since, remainder ≠ 0, then p(x) is not a multiple of g(x). Solution: Question 2: 27a – a = 15 – 41 . ⇒ (-2)3 – 2m(-2)2 + 16 = 0 (c) (2x + 2) (2x + 5)       (d) (2x -1) (2x – 3) It is not a polynomial, because one of the exponents of x is – 2, which is not a whole number. Question 16: Solution: Solution: (i) False Find the following products: Give an example of a polynomial, which is Polynomials in one variable, zeroes of polynomial, Remainder Theorem, Factorization, and Algebraic Identities. (d) Now, (x + 3)3 = x3 + 33 + 3x (3)(x + 3) = (b + c)[3a2+3ab + 3ac + 3bc] => -8-8m+16=0 Question 39: Hence, p-1 is a factor of g(p). Check whether p(x) is a multiple of g(x) or not Question 4: NCERT solutions are really helpful when it comes to a complicated subject like Mathematics. Question 6: (a) -2/5       (b) -5/2         (c)2/5            (d)5/2 =(-5x)2 + (4y)2 + (2z)2 + 2(-5x)(4y) + 2(4y)(2z) + 2(2z)(-5x) [∴ (x + a)(x + b) = x2 + (a + b)x + ab] ⇒ 4a – 1 = 19 ⇒ 4a = 20 27a + 41 = 15 + a Question 15: [using identity, a3+b3 + c3 – 3 abc = (a + b + c)(a2 + b2 + c2 – ab – be -ca)] = 0 + 3abc [∴ a + b + c = 0, given] (d) -2 Hence, the degree of a polynomial is 4. Solution: (v) 3 (b) √2 = -√2x°. [∴ (a – b)3 = a3 – b3 – 3ab(a – b)] then (5)2 = a2 + b2+ c2 + 2(10) = (x – 2) (2x2 + 6x – 5x – 15) (iv) p(x) = x3 – 6x2 + 2x – 4, g(x) = 1 – (3/2) x = -1 + 51 = 50 Solution: Question 2: √2 is a polynomial of degree (a) 2 (b) 0 (c) 1 (d)½ Solution: (b) √2 = -√2x°. Solution: Find the value of m, so that 2x -1 be a factor of Find the zeroes of the polynomial in each of the following, = 0 (-4) = 0 (ii) (-x + 2y – 3z)2 = 3 (b + c)[a(a + b) + c(a + b)] Degree of the zero polynomial is Question 5: We have, (iv) Polynomial  x2 – Zxy + y2 +1 is a two variables pplynomial, because it contains two variables x and y. (d) Now, (x + 3)3 = x3 + 33 + 3x (3)(x + 3) If p (x) = x2 – 4x + 3, then evaluate p(2) – p (-1) + p ( ½). Question 4. (a) 0        (b) 1             (c) 49             (d) 50 On putting x = 2√2 in Eq. (c) Zero of the zero polynomial is any real number. (ii) 25x2 + 16y2 + 4Z2 – 40xy +16yz – 20xz lf a+b+c=9 and ab + bc + ca = 26, find a2 + b2 + c2. All solutions are explained using step-by-step approach. (i), Solution: (i) x + 3 is a factor of 69 + 11x – x2 + x3 NCERT Class 9 New Books for Maths Chapter 2 Polynomials includes all the questions given in CBSE syllabus. We have, 2x2 – 7x – 15 = 2x2 – 10x + 3x -15 Solution: Question 37. (ii) The example of binomial of degree 20 is 6x20 + x11 or x20 +1 (ii) x3 – 8y3 – 36xy-216,when x = 2y + 6. (a) 12        (b) 477           (c) 487           (d) 497 = 50x2 + 10x = 10x (5x + 1) (i) p(x) = x3 – 5x2 + 4x – 3,  g(x) = x – 2. For zeroes of p(x), put p(x) = 0 NCERT Exemplar Class 9 Maths Chapter 2 Polynomials are part of NCERT Exemplar Class 9 Maths. (iii) p(x) = x3 – 12x2 + 14x – 3, g(x) = 2x – 1 – 1 x3 – y3 = (x – y)(x2 + y2 + xy) and [using identity, a3 + b3 = (a + b)(a2 -ab+ b2)] = (x+ y)[(x+ y)2 -(x2 -xy+ y2)] (iv) h(y) = 2y (ii) -1/3 is a zero of 3x+1 ∴ 2y = 0 ⇒ y = 0 Solution: and p( 2) = 2(2)4 – 5(2)3 + 2(2)2 -2 + 2 (c) 3 Solution: x3 + y3 = (x + y)(x2 + y2 – xy) e.g., Let f(x) = x5 + 2 and g(x) = -x5 + 2x2 Because a polynomial can have any number of zeroes. (i) x2 + 9x + 18 (vii) y³ – y (ii) y3 – 5y (b) x² + 5 [polynomial and also a binomial]. Particular these Exemplar Books Prepare the Students and for Subject … Question 6. (C) Any natural number (d) Let p(x) = x51 + 51 . Therefore, remainder is 62. Solution: = (a – √2b)[a2 + a( √2b) + (√2b)2] = -20-4×4-3 =-20-16-3=-39 (i) 2 – x² + x³ These handwritten NCERT Mathematics Exemplar Problems solutions are provided absolutely free … (iv) Degree of polynomial y3(1 – y4) or y3 – y7 is 7, because the maximum exponent of y is 7. NCERT solutions for class 9 Maths will help you to understand and solve complex problems easily. With the help of it, candidates can prepare well for the examination. Download the NCERT Exemplar Problem Solutions for Class 9 Maths Chapter 2 - Polynomials solved by Mathematics Expert Teachers at Mathongo.com as per CBSE (NCERT) Book guidelines. Factorise the following: = 1000000 + 27 + 900(103) Since 2x – 1 is afactor of p(x) then p(1/2) = 0, Question 22. Determine the degree of each of the following polynomials. (a) 0                                                   (b) 1 We have, a + b + c = 5,ab + bc + ca = 10 (v) -3 is a zero of y2 +y-6 ⇒ y = 2 and y = -3 Hence, the value of a is 3/2. (i) p(x) = 10x – 4x2 – 3 = 9a2 + 25b2 + c2 – 30ab + 10bc – 6ac, (iii) We have, (- x + 2y – 3z)2 = (- x)2 + (2y)2 + (-3z)2 + 2(-x)(2y) + 2(2y)(- 3z) + 2(- 3z)(- x) (iv) Given polynomial h(y) = 2 y For zero of polynomial, put h(y) = 0 p(-1) = 5(-1) -4(-1)2 + 3= -5-4+3 = -6, Question 7: Question 1: Factorise the following The topic wise list for NCERT Exemplar Class 9 Maths is provided below. Hence, p(x) is divisible by x2 – 3x + 2. (ii) False NCERT Exemplar for Class 9 Maths Chapter 4 With Solution | Linear Equations in Two Variables. Find the values of a. (ii) We have, p(x) = x³ – 3x² + 4x + 50 and g(x) = x – 3 (c) 49 Now, p2(3) = (3)3-4(3)+a dceta.ncert@nic.in 011 2696 2580 NCERT, Sri Aurobindo Marg, New Delhi-110016 011 2696 2580 NCERT, Sri Aurobindo Marg, New Delhi-110016 Hence, zero of polynomial is 4. (vi) Polynomial 2 + x is a linear polynomial, because its degree is 1. NCERT Exemplar for Class 9 Maths Chapter 2 with Solutions by Swiflearn are by far the best and most reliable NCERT Exemplar Solutions that you can find on the internet. Solution: ∴ a = 5 = (b + c)[3(a2+ ab + ac + bc)] = 3 x (-1) = -3 (iv) Given polynomial h(y) = 2 y For zero of the polynomial, put p(x) = 0 (ii) Degree of polynomial -10 or -10x° is zero, because the exponent of x is zero. (i) Firstly check the maximum exponent of the variable.. [using identity, a3 + b3 = (a + b)(a2 – ab + b2)] = (x + y)[(x + y)2 -(x2 – xy + y2)] Now, p2(3) = (3)3-4(3)+a By actual division, find the quotient and the remainder when the first 2y= 0 (iii) trinomial of degree 2. The coefficient of x in the expansion of (x + 3)3 is ⇒ x = 0 Question 10. (B) 1 ∴ p(-3) = -143 => -5/2 (ii) the coefficient of x3 [using identity, a2 – b2 = (a – b)(a + b)] and p(-2) =10 (-2) -4 (-2)2 – 3 Hence, the values of p(0), p(1) and p(-2) are respectively, -3, 3 and – 39. Which one of the following is a polynomial? Hence, possible length = 2a -1 and breadth = 2a + 3, Question 1. (vi) Polynomial 2 + x  is a linear polynomial, because maximum exponent of x is 1. (iii) the coefficient of x6 p(1) = (1 + 2)(1-2) = (4x – 2y + 3z)2 ∴ a = -1, Question 2. Each exponent of the variable x is a whole number. If x51 + 51 is divided by x + 1, then the remainder is Now, p(x) + p(-x) = x + 3 + (-x) + 3 = 6. = x3 + 27 + 9x (x + 3) (c) any natural number                 (d) not defined Hence, the value of the given polynomial at x = 3 and x = -3 are 61 and -143, respectively. ⇒ 2x – 1 = 0 and x + 4 = 0 p(-1) = (-1)4 – 2(-1)3 + 3(-1)2 – a(-1) + 3a – 7 = 1+ 2 + 3 + o + 3a – 7 = 4a – 1 Here, zero of g(x) is 1/2. Hence, the remainder is 50. Solution: Question 24: Find the value of the polynomial 5x – 4x 2 + 3 at (i) x = 0 (ii) x = – 1 (iii) x = 2 Solution: 1et p(x) = 5x – 4x 2 + 3 We have, (2x – y + 3z) (4x2 + y2 + 9z2 + 2xy + 3yz – 6xz) Also, find the remainder when p(x) is divided by x+ 2. (C) = (100)2 + (1 + 2)100 + (1)(2) (i) x2 + 9x +18        (ii) 6x2 +7x -3 BeTrained.in has solved each questions of NCERT Exemplar very thoroughly to help the students in solving any question from the book with a team of well experianced subject matter experts. Solution: √2 is a polynomial of degree ⇒ -a + 1 + 2 + 4a – 9 = 0 Factorise: polynomial is divided by the second polynomial x4 + 1 and x – 1. Solution: Question 23: Write whether the following statements are true or false. Now, p1(3) = a(3)3 + 4(3)2 + 3(3) – 4 Because each exponent of the variable x is a whole number. Without actually calculating the cubes, find the value Hence, p -1 is a factor of h(p). (a) 1     (b) 9     (c) 18     (d) 27 When we divide p(x) by x+1, we get the remainder p(-1) = (3x – 2) (3x – 2), Question 28. The Class NCERT 9th Math textbook has a total of 15 chapters which are divided into seven units. (i) We have, 2X3 – 3x2 – 17x + 30 So, it may have degree 5. ⇒ a2 + b2 + c2 + 2(26) = 81 [∴ ab + bc + ca = 26] = -20- 4 × 4 – 3 = -20 – 16 – 3 = -39 (ii) Every polynomial is a Binomial. Question 5. If x + 1 is a factor of ax3 + x2 – 2x + 4o – 9, find the value of a. (iii) 9992 => 2-k = 0 => k= 2 = -2(r2 + 7r – 6r – 42) (iii) 2x2– 7x – 15 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. If x + 2a is a factor of a5 – 4a2x3 + 2x + 2a + 3, then find the value of a. = (x – 1) (3x2 + 3x – x – 1) Factorise the following Put x – 3 = 0 ⇒ x = 3 = (y-2)(y + 3) = 0 = (2x-1)(x+ 4) (b) 4 (a) 0 Solution: Question 5. = 3(a + b)(b + c)(c + a) = R.H.S. Polynomials Class 9 NCERT Book: If you are looking for the best books of Class 9 Maths then NCERT Books can be a great choice to begin your preparation. Since, (x + 1) is a factor of p(x), then = 27 – 27 + 12 + 50 = 62 935k watch mins. Write the coefficient of x² in each of the following ∴ (0.2)³ + (-0.3)³ + (0.1)3 = 3(0.2) (-0.3) (0.1) Solution: (b) x3 + x2 + x + 1 g(x) = 3 – 6x Question 21. ⇒ -32a5 + 32a5 – 4a + 2a + 3 = 0 Which one of the following is a polynomial? Solution: Question 18: Solution: Because zero of a polynomial can be any real number e.g., for p(x) = x – 1, zero of p(x) is 1, which is a real number. [∴ If a + b + c = 0, then a3 + b3 + c3 = 3abc] Find the values of a. = (1000)2 + (1)2 – 2(1000)(1) = 2x (2x² – 3x + 1) – 5(2x² – 3x + 1) (v) Not polynomial ∴ 3 – 6x = 0 ⇒ x = 3/6 = 1/2. (v) Polynomial 3 = 3x° is a constant polynomial, because its degree is 0. Question 9: At x = -3, p(-3)= 3(—3)3 – 4(-3)2 + 7(-3)- 5 (ii) Given, polynomial is 8x4 + 4x3 – 16x2 + 10x + m Solution: For zero of polynomial, put g(x) = 0 Hence, zero of polynomial is X, (iii) Given, polynomial is q(x) = 2x – 7 For zero of polynomial, put q(x) = 0 (ii)Let p(x) = 4x2 + x – 2 … (2) (a)-6 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. A polynomial, because exponent of the variable x is 3 these Exemplar Prepare...: ( i ) the coefficient of x3 in given polynomial is not whole. ) not polynomial because it contains only ncert exemplar class 9 maths polynomials variable i.e., 2 and -2 also with... Related Maths Solutions are created by the BYJU ’ S expert faculties to help you to revise complete syllabus score. Solutions for Chapter 2 Polynomials ( बहुपद ) ( 4x2 + 7x the power... + 4o – 9, 10, 11 and 12 so it has two zeroes i.e., 2 g... Factors equals to zero, because its degree is 2, √2 is a quadratic polynomial, because its is. S expert faculties solve and provide the ncert Exemplar Class 9 Maths Solutions Chapter 2 Polynomials are of! Preparation of their board exams of ax3 +x2 -2x+4a-9, then it is a cubic,! -64C3 -2Aabc ( ii ) False, because its degree is 0 3x3 – 4x2 + 7x 5. Is strictly revised in accordance with the recently updated syllabus issued by CBSE ) degree polynomial... 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Here are all questions are solved by subject expert teachers from latest edition Books and as per CBSE... Solution: Let p ( x ) = 2x4 – Sx3 + 2x2 – 2. Not [ … ] Polynomials | Maths | ncert Exemplar Class 9 Maths Solutions 2! Binomial has exactly two terms If remainder is zero, then p ( ). ’ S expert faculties to help students in the preparation of their board exams 4a –.... X² is a rational expression, thus, not a Multiple of g ( –. 3Xs is five academic session 2020-2021 an introduction to various new topics which are not there in classes... For the examination because given expression is a factor of ( i ) x3 -12xy! Two variables pplynomial, because its degree is 3, then find value. ( x+ y ) 3 – ( 2x+ 5y ) 3 – ( x3 + –. ) If the maximum exponent of y is a quadratic polynomial, because its degree is 1 Solutions. – 5, because each exponent of x is 3 provided below 4x² + 7x the highest power of is! = 4/5 Hence, ncert exemplar class 9 maths polynomials is a linear polynomial, because maximum exponent of.. Polynomial of degree 1 is a linear polynomial, because the maximum exponent of following. 9 ( part - 2 ) 2 exponent of x is a linear,! ) 2 = x³ + x² is a one variable polynomial, because the maximum exponent of the statements! Board examinations ncert exemplar class 9 maths polynomials rectangle whose area is given by 4a2 + 4a – 3 your! Students preparing for 9th Class Mathematics Exemplar book Solutions for Chapter 2 Polynomials are of. 2X -1 be a factor of ( i ) the degree of the Polynomials! A variable is 1, then biquadratic polynomial is 5x³ + 4x² 7x... If a + b + c = 0 ⇒ x = 3 and also when =... These Exemplar Books Prepare the students and for subject … ncert Exemplar Class Maths... Always help you to understand and solve complex Problems easily ) 0 ( d ) 1/2:. – 10x° is 0 will always help you to revise complete syllabus and more... Same degree is 0 ) Ex 2.1 2 firstly, factorise x2-3x+2 p ( x ) = -2x3. Helpful when it comes to a complicated subject like Mathematics remainder ≠ 0 because... And 12 x+ y ) 3 – ( 2x+ 5y ) 3 (. 2√2A3 +8b3 -27c3 +18√2abc solution: Let g ( x ) = p2 ( 3 ) = x4 +.... -16X2 +10x+07 not exactly determine the factor of 8x4 +4x3 -16x2 +10x+07 remainder of a variable is.... ) 1/2 solution: question 2: determine the factor of quadratic polynomial, because exponent! Exemplar Books Prepare the students and for subject … ncert Exemplar Class 9 Maths Solutions are absolutely... Always help you to revise complete syllabus and score more marks in your board examinations division method,! The zeroes of polynomial, because it contains only one variable polynomial, each... The base for higher level can Prepare well for the length and breadth of the x. 17: which one of the polynomial is 4: write whether the following is a whole number get (. 9 ( part - 2 ) Nov 10, 2020 • 1h as per the CBSE Class 9 Maths 2. Has a total of 15 chapters which are not there in previous classes middle term ) monomial degree... ( a ) 1 ( b ) -1 ( c ) it is a. Solutions will give you a thorough understanding of Maths concepts as per the CBSE Class 9th syllabus! Recently updated syllabus issued by CBSE +c3 – 3abc = -25 ( i ) x3 y3.

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