= 7y(5y + 4) – 3(5y + 4) = (5 y + 4)(7y – 3) We have, (x + 4) (x + 10) = x2+(4 + 10) x + (4 x 10) (i) p(x) = 3x + 1,x = –\(\frac { 1 }{ 3 }\) = x2 + (2y)2 + (4z)2 + 2 (x) (2y) + 2 (2y) (4z) + 2(4z) (x) (iii) Given that p(x) = x3 = 2√2 = (2x + 3)(3x – 2) (iii) 104 x 96 (iv) The given polynomial is √2 x – 1. Solutions to all NCERT Exercise Questions and Examples of Chapter 2 Class 9 Polynomials are provided free at Teachoo. Variables and expression are called as indeterminate and coefficients. ∴ p(3) = (3)3 – 4(3)2 + 3 + 6 = (3x + y)2 = (1000)3– (2)3 – 3(1000)(2)(1000 – 2) = 4k[3y2 – 3y + 5y – 5] (ii) y2 + √2 ∴ p(0) = (0 – 1)(0 + 1) = (-1)(1) = -1 Extra questions based on the topic Number System. ⇒ p(1) = k + 2 = 0 Chapter-wise NCERT Solutions for Class 9 Maths Chapter 2 Polynomials solved by Expert Teachers as per NCERT (CBSE) Book guidelines. is given, we can find the other two trigonometric ratios (i.e. Since,( \(-\frac { 490 }{ 9 }\)) ≠ 0 = 1000000000 – 8 – 6000000 +12000 ∴ (-12)3 + (7)3 + (5)3 = 3[(-12)(7)(5)] The coefficient of x2 is 0. The coefficient of x2 is \(\frac { \pi }{ 2 }\). (i) Here, p(x) = x2 + x + k ∴ p(-1) = (-1)3 + 3(-1)2 + 3(-1) +1 (iv) x + π It is a polynomial in one variable i.e., y = (2y)2 + 2(2y)(1) + (1)2 Thus, zero of x – 5 is 5. (ii) We have, p(x) x3 + 3x2 + 3x + 1 and g(x) = x + 2 (iii) p(2) = 5(2) – 4(2)2 + 3 = 10 – 4(4) + 3 = (2x)2 + (3y)2 + (- 4z)2 + 2 (2x) (3y) + 2 (3y) (- 4z) + 2 (- 4z) (2x) Question 2. (ii) p (x) = 5x – π, x = \(\frac { 4 }{ 5 }\) (i) p(0) = 5(0) – 4(0)2 + 3 = 0 – 0 + 3 = 3 We hope the NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1, help you. Rearranging the terms, we have x3 – x – 2x2 + 2 (ii) 8a3 -b3-12a2b+6ab2 These ncert book chapter wise questions and answers are very helpful for CBSE board exam. Solution: (iv) 3 = 4x (3x – 1 ) -1 (3x – 1) Evaluate the following products without multiplying directly Using the identity, Question 1. (iv) p (x) = kx2 – 3x + k Using identity, (i) 4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz Use suitable identities to find the following products = (y – 1)[2y(y + 1) + 1(y + 1)] (i) x + 1 Class 9 Mathematics Notes for FBISE. = -14 + 13 Ex 2.1 Class 9 Maths Question 4. [Using (a + b)(a -b) = a2– b2] (i) We know that Here, exponent of every variable is a whole number, but x10 + y3 + t50 is a polynomial in x, y and t, i.e., in three variables. Solution: Using identity, ⇒ cx + d = 0 ⇒ cx = -d ⇒ \( x =-\frac { d }{ c }\) (ii) 35y2+ 13y -12 = 35y2 + 28y – 15y -12 (vii) P (x) = 3x2 – 1, x = – \(\frac { 1 }{ \sqrt { 3 } }\),\(\frac { 2 }{ \sqrt { 3 } }\) The highest = (3 – 5a) (3 – 5a) (3 – 5a), (iv) 64a3 -27b3 -144a2b + 108ab2 Question 10. ∴ p(a) = (a)3 – a(a)2 + 6(a) – a ∴ p (-1) = (-1)3 + (-1)2 + (-1) + 1 . Since, p(1) = 2(1)2 + k(1) + √2 (ii) 4 – y2 ⇒ (x + y)(x2 + y2 – xy) = x3 + y3 Thus, zero of 3x is 0. NCERT Solutions for Class 9 Maths: The Class 9 Maths textbook solutions of exercises for all 15 chapters are included in this article. (i) We have, 99 = (100 -1) Let p(x) = x3 + 3x2 + 3x +1 (iii) The degree of y + y2 + 4 is 2. Along with recalling the knowledge of linear … Chapter-9 Chapter-2 Sol. (iii) Let p (x) = x4 + 3x3 + 3x2 + x + 1 . Solution: ⇒ 3x – 2 = 0 (ii) We have, p(x) = 5x – π So, the degree of the polynomial is 2. (iii) x3 + 13x2 + 32x + 20 (i) 9x2 + 6xy + y2 = (x + 1)(x2 – 4x – 5) ⇒ k = \(\frac { 3 }{ 4 }\), Question 4. Chapter -1 Sol. = \(\frac { 1 }{ 2 }\) (x + y + z)[2(x2 + y2 + z2 – xy – yz – zx)] Solution: ∴p(0) = 2 + 0 + 2(0)2 – (0)3 Ex 2.1 Class 9 Maths Question 2. Since, p(1) = k(1)2 – (1) + 1 We know that if x + y + z = 0, then x3 + y3 + z3 = 3xyz ⇒ x = \(\frac { 2 }{ 3 }\) So, the degree of the polynomial is 3. (iii) We have 3 √t + t√2 = 3 √t1/2 + √2.t = (3y + 5z)[(3y)2 – (3y)(5z) + (5z)2] Teachoo is free. (iii) x = 2 + 0 + 0 – 0=2 Thus, the value of 5x – 4x2 + 3 at x = -1 is -6. Question 2. (iii) x2 – \(\frac { { y }^{ 2 } }{ 100 }\) (i) p(y) = y2 – y +1 Thus, 2y3 + y2 – 2y – 1 Important questions in Number systems with video lesson. (ii) 2x2 + 7x + 3 p(1) = k(1)2 – 3(1) + k (vii) 7x3 Since, p(0) = 0, so, x = 0 is a zero of x2. Here we have given NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1. (ii) x3 – y3 = (x – y) (x2 + xy + y2) Class-IX CHAPTER – 1 Number System (Maths Assignment) 1. = x3 + x2 – 4x2 – 4x – 5x – 5 , = 10000 + (-9) + 20 = 9120 (ii) x = – 1 NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. 12x2 – 7x + 1 = 12x2 – 4x- 3x + 1 x3 + y3 = (x + y)(x2 – xy + y2) [Using (a – b)3 = a3 – b3 – 3ab (a – b)] CBSE Class 11 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and … [Using a3 + b3 + 3 ab(a + b) = (a + b)3] = (y – 1)(y + 1)(2y + 1) = 9x2 – x – 20, Question 2. Login to view more pages. (ii) 2 – x2 + x3 ∴ p(o) = (0)2 = 0 p( 2) = 2 + 2 + 2(2)2 – (2)3 = -1 + 1 – 1 + 1 (ii) (102)3 = 8a3 – 27b3 – 36a2b + 54ab2, Question 7. Hence, if x + y + z = 0, then Chapter 13 Geometrical Constructions. (v) x10+ y3+t50 Since, p(1) = 0, so x = 1 is a zero of x2 -1. Determine which of the following polynomials has (x +1) a factor. For example, if you are weak in class 9 maths, you can’t make a great career in the field of engineering and mathematics. All these questions are based on the important fundamental concepts given in NCERT Class 9 Maths. So, (x + 1) is not a factor of x3 – x2 – (2 + √2) x + √2. = 1 – 1 + 1 – 1 + 1 [∵ (a2 – b2) = (a + b)(a-b)] Hence, verified. Download free printable assignments for CBSE Class 9 Mathematics with important chapter wise questions, students must practice NCERT Class 9 Mathematics assignments, question booklets, workbooks and topic wise test papers with solutions as it will help them in revision of important and difficult concepts Class 9 Mathematics.Class Assignments for Grade 9 Mathematics, … power of the variable y is 2. (ii) ∵ (x – y)3 = x3 – y3 – 3xy(x – y) = a3 – a3 + 6a – a = 5a Since p(-1) = 0, so, x = -1, is also a zero of x2 – 1. = (2y – 1)(2y – 1 ), Question 4. FREE Downloadable! (i) We have, (-12)3 + (7)3 + (5)3 Mathematics Part - II Solutions Textbook Solutions for Class 9 Math. (i) x = 0 (i) We have, p(x) = x + 5. We have, p(x) = x3 – ax2 + 6x – a and zero of x – a is a. Thus, the possible length and breadth are (7y – 3) and (5y + 4). Thus, the value of 5x – 4x2 + 3 at x = 2 is – 3. (iii) 27-125a3 -135a+225a2 = – 5x – 4x2 + 3 = -9 + 3 = -6 sin θ and tan θ) without evaluating θ. Thus, zero of cx + d is \(-\frac { d }{ c }\), Question 1. ⇒ (x + y)[(x + y)2-3xy] = x3 + y3 (iv) Since, 3 = 3x° [∵ x°=1] NCERT Book NCERT Sol. After an in-depth analysis, our expert panel has drafted the solutions so that students of class 9 can easily refer to them during their exams or to complete their homework. [Hint See question 9] = 1000000 + 8 + 600(100 + 2) (iii) p (x) = x3 – 4x2 + x + 6, g (x) = x – 3 (iii) The zero of x is 0. The coefficient of x2 is 1. Thus, 6x2 + 5x – 6 = (2x + 3)(3x – 2), (iv) We have, 3x2 – x – 4 = 3x2 – 4x + 3x – 4 They give a detailed and stepwise explanation of each answer to the problems given in the exercises in the NCERT … (i) The given polynomial is 5x3 + 4x2 + 7x. They are in a list with arrows. = 3x(2x + 3) – 2(2x + 3) Thus, the required remainder is \(-\frac { 27 }{ 8 }\) . = (x + 1)(x2 + 2x + 10x + 20) (vii) We have, p(x) = cx + d. Since, p(x) = 0 State reasons for your answer. It is a complete package of solutions to problems of your really tough book. (iv) 1 + x (v) The zero of 5 + 2x is \(-\frac { 5 }{ 2 }\) . (v) The degree of 3t is 1. = (3x)2 + 2(3x)(y) + (y)2 Get here MCQs on Class 9 Maths Chapter 2- Polynomials with answers. ⇒ p(3) = 0, so g(x) is a factor of p(x). = \(\frac { 1 }{ 2 }\) (x + y + 2)(x2 + y2 + y2 + z2 + z2 + x2 – 2xy – 2yz – 2zx) Thus, the required remainder is 5a. = -1 – 1 + 2 + √2 + √2 Ex 2.1 Class 9 Maths Question 3. p(1) = (1 – 1)(1 +1) = (0)(2) = 0 (i) ∵ (x + y)3 = x3 + y3 + 3xy(x + y) Solution: Learn about the degree of a polynomial and the zero of a polynomial with related Maths solutions. (i) The given polynomial is 2 + x2 + x. Thus, zero of 2x + 5 is \(\frac { -5 }{ 2 }\) . (v) p (x) = x2, x = 0 = (2 a + b)3 = (y – 1)(2y2 + 2y + y + 1) Since, p(x) = 0 = (100)3 – 13 – 3(100)(1)(100 -1) = (2a – b)3 Verify whether the following are zeroes of the polynomial, indicated against them. Unit 1 - Matrices & Determinants. Solution: (iv) Given that p(x) = (x – 1)(x + 1) = x2 + 4y2 + 16z2 + 4xy + 16yz + 8 zx, (ii) (2x – y + z)2 = (2x)2 + (- y)2 + z2 + 2 (2x) (- y)+ 2 (- y) (z) + 2 (z) (2x) Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.5 Exercise 1.6 ... Class 9 Mathematics Notes are free and will always remain free. (iv) We have, p(x) = (x + 1)(x – 2) Thus, the possible dimensions of the cuboid are 4k, (3y + 5) and (y -1). Solution: = ( 100)2 + (3 + 7) (100)+ (3 x 7) The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.. For a better understanding of this chapter… = \(\frac { 1 }{ 2 }\)(x + y + z)[(x – y)2+(y – z)2+(z – x)2] So, the degree of the polynomial is 0. = -π3 + 3π2 + (-3π) + 1 [Using (x + a)(x + b) = x2 + (a + b)x + ab] (i) 4 x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz (v) 5 + 2x = x3 + y3 + z3 – 3xyz = L.H.S. Thus, the value of 5x – 4x2 + 3 at x = 0 is 3. (x+ a) (x+ b) = x2 + (a + b) x+ ab. Solution: 27x3 + y3 + z3 – 9xyz = (3x)3 + (y)3 + (z)3 – 3(3x)(y)(z) = 2 x \(\frac { 1 }{ 2 }\) x (x + y + z)(x2 + y2 + z2 – xy – yz – zx) ⇒ p(-1) = 0, so g(x) is a factor of p(x). (v) (- 2x + 5y – 3z)2 (i) Let p (x) = x3 + x2 + x + 1 Factorise each of the following = (y – 1)(2y2 + 3y + 1) We have, 27y3 + 125z3 = (3y)3 + (5z)3 (i) We have, p (x)= 2x3 + x2 – 2x – 1 and g (x) = x + 1 P(1) = 2 + 1 + 2(1)2 – (1)3 = 8x3 + 1 + 6x(2x + 1) (i) p (x)= 2x3 + x2 – 2x – 1, g (x) = x + 1 (vi) We have, p(x) = ax, a ≠ 0. (iii) We have, p(x) = 2x + 5. Question 3. Find p (0), p (1) and p (2) for each of the following polynomials. [Using a3 – b3 – 3 ab(a – b) = (a – b)3] Since, p(-1) = 0, so, x = -1 is a zero of (x + 1)(x – 2). = \(\frac { 1 }{ 2 }\) (x + y + 2)[(x2 + y2 – 2xy) + (y2 + z2 – 2yz) + (z2 + x2 – 2zx)] = (- √2x + y + 2 √2z) (- √2x + y + 2 √2z), Question 6. (iii) We have, p(x) = x2 – 1 = x2 (x + 1) – 4x(x + 1) – 5(x + 1) Prepare effectively for your Maths exam with our NCERT Solutions for CBSE Class 9 Mathematics Chapter 2 Polynomials. (v) We have, p(x) = 3x. (ii) x4 + x3 + x2 + x + 1 Evaluate the following using suitable identities (iii) p (x) = x2 – 1, x = x – 1 Question 13. (x + a) (x + b) = x2 + (a + b) x + ab = 2y2(y – 1) + 3y(y – 1) + 1(y – 1) Find the zero of the polynomial in each of the following cases = (- √2x + y + 2 √2z)2 Thus, the required remainder = 1. Question 3. (vi) p (x)= ax, a≠0 (i) We have, (v) We have x10+ y3 + t50 [Using a2 + 2ab + b2 = (a + b)2] What are the possible expressions for the dimensions of the cuboids whose volumes are given below? (i) We have, 3x2 – 12x = 3(x2 – 4x) = (3y + 5z)(9y2 – 15yz + 25z2), (ii) We know that After the completion of chapters from NCERT Books and Exemplar Books, students should go for Assignments. (iv) y+ \(\frac { 2 }{ y }\) (iii) p (x) = 2x + 5 = 27 – 4(9) + 3 + 6 = x(3x – 4) + 1(3x – 4) = (3x – 4)(x + 1) = [(x)2 – (1)2](x – 2) (vi) The degree of r2 is 2. [Using a3 + b3 + 3 ab(a + b) = (a + b)3] Give one example each of a binomial of degree 35, and of a monomial of degree 100. (ii) p(x)= x3 + 3x2 + 3x + 1, g (x) = x + 2 If x + y + z = 0, show that x3 + y3 + z3 = 3 xyz. (iii) (- 2x + 3y + 2z)2 ∴ \(p(\frac { 1 }{ 2 } )\quad =\quad 2(\frac { 1 }{ 2 } )+1=\quad 1+1\quad =\quad 2\) (ii) Area 35y2 + 13y – 12 = 9a2 + 49b2 + c2 – 42ab + 14bc – 6ac, (v)(- 2x + 5y- 3z)2 = (- 2x)2 + (5y)2 + (- 3z)2 + 2 (- 2x) (5y) + 2 (5y) (- 3z) + 2 (- 3z) (- 2x) = 4[3ky2 + 2ky – 5k] = 4[k(3y2 + 2y – 5)] ⇒ p (- 1) = 0 (iv) √2 x – 1 = x2 + 14x+40, (ii) We have, (x+ 8) (x -10) (ii) 2x2 + y2 + 8z2 – 2√2xy + 4√2yz – 8xz (ii) Given that p(t) = 2 + t + 2t2 – t3 = (x + y + z)(x2 + y2 + z2 – xy – yz – zx) So, the degree of the polynomial is 1. 1et p(x) = 5x – 4x2 + 3 Question from very important topics are covered by NCERT Exemplar Class 9.. You also get idea about the type of questions and method to answer in your Class 9th … and zero of 7 + 3x is \(-\frac { 7 }{ 3 }\). Solution: In this article, you will get the MCQs on Class 9 Maths Chapter 4: Linear Equations in Two Variables. (i) 2 + x2 + x Get NCERT solutions for Class 9 Maths free with videos of each and every exercise question and examples. = (2x + 3y – 4z)2 = (2x + 3y + 4z) (2x + 3y – 4z), (ii) 2x2 + y2 + 8z2 – 2√2xy + 4√2yz – 8xz (ii) x – x3 (i) (x+2y+ 4z)2 = (3)3 – (5a)3 – 3(3)(5a)(3 – 5a) ⇒ x = -5. Solution: ∴ p(1) = (1)2 – 1 = 1 – 1=0 Solution: Solution: Answers to each and every question is explained in an easy to understand way, with videos of all the questions. In this NCERT Solutions for Class 9 Maths Chapter 2, Polynomials, you learn about the definition of Polynomials which comes from the word “poly” which means “many” and the word “nominal” which means “term”. NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.4; NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.3; NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Ex 10.2; NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.2 Hence, verified. = -2 + 1 + 2 -1 = 0 Thus, 7 + 3x is not a factor of 3x3 + 7x. Write the degree of each of the following polynomials. = 2 + k + √2 =0 Since, p(x) = 0 We have, (x + y)3 = x3 + y3 + 3xy(x + y) …(1) Solution: (ii) 95 x 96 ! Solution: (i) We have, 9x2 + 6xy + y2 ⇒ x3 + y3 + 3xy(-z) = -z3 [∵ x + y = -z] Solution: Verify x3 + y3 + z3 – 3xyz = (x + y + z)(x2 + y2 + z2 – xy – yz – zx) Solution: We have, (3x)3 + (y)3 + (z)3 – 3(3x)(y)(z) ∴ (998)3 = (1000-2)3 Class 9 Maths Chapter 2 Polynomials This chapter guides you through algebraic expressions called polynomial and various terminologies related to it. (vii) The degree of 7x3 is 3. Chapter-3 Chapter-11 Sol. (ii) p (x) = 2x2 + kx + √2 However, it is possible to avoid such a scenario by taking authentic NCERT solutions for class 9 maths from a reliable source. Exercise 13.1 Solution. (i) x3 + y3 = (x + y)-(x2 – xy + y2) Since, p(1) = (1)2 +1 + k (ii) (28)3 + (- 15)3 + (- 13)3 Students first revise all the topics from NCERT book and then Solve the sums in this worksheet. We have, (i) Abmomial of degree 35 can be 3x35 -4. (iii) 3 √t + t√2 (i) 8a3 +b3 + 12a2b+6ab2 = 1000300 – 30001 = 970299, (ii) We have, 102 =100 + 2 (ii) Here, p (x) = 2x2 + kx + √2 (i)We have, 103 x 107 = (100 + 3) (100 + 7) ∴ 3x3 + 7x is not divisib1e by 7 + 3x. ∴ p(0) = (0)3 + 3(0)2 + 3(0) + 1 P(2) = (2 – 1)(2 + 1) = (1)(3) = 3. Solution: Ex 2.1 Class 9 Maths Question 5. Thus, the possible length and breadth are (5a – 3) and (5a – 4). = 994011992, Question 8. p(2) = (2)2 – 2 + 1 = 4 – 2 + 1 = 3 (viii) p (x) = 2x + 1, x = \(\frac { 1 }{ 2 }\) Homework Help with Chapter-wise solutions and Video explanations. ⇒ p(-2) ≠ 0, so g(x) is not a factor of p(x). p(-π) = (-π)3 + 3(- π)22 + 3(- π) +1 (i) 27y3 + 125z3 (iv) The zero of x + π is -π. Since, x + y + z = 0 Question 16. ∴ p(-1) = (-1 +1) (-1 – 2) = (0)(- 3) = 0 = 2k – 3 = 0 = (x + 1)(x – 5)(x + 1) (iii) 6x2 + 5x – 6 So, (x + 1) is not a factor of x4 + x3 + x2 + x+ 1. Exercise 14.1 Solution. So, it is a quadratic polynomial. = 1000000000 – 8 – 6000(1000 – 2) (iii) y + y2+4 CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. (ii) 64m3 – 343n3 = (4a)3 – (3b)3 – 3(4a)(3b)(4a – 3b) In this … (vi) r2 (ii) x3 – 3x2 – 9x – 5 Solution: These NCERT solutions are created by the BYJU’S expert faculties to help students in the preparation of their board exams. (ii) x – \(\frac { 1 }{ 2 }\) = 1000000 – 1 – 300(100 – 1) = (y – 1)(y + 1)(2y +1), Question 1. The highest power of the variable x is 3. Chapter - 3 Pair of Linear Equations. ∴ 1023 = (100 + 2)3 (vi) p (x) = 1x + m, x = – \(\frac { m }{ 1 }\) Question 2. ∴ p (- 1) =(- 1)3- (-1)2 – (2 + √2)(-1) + √2 = x2 – 2x – 80, (iii) We have, (3x + 4) (3x – 5) This solution is strictly revised in accordance … (v) We have, p(x) = x2 = (x + 1)(x2 – 5x + x – 5) = 10000 + 1000 + 21=11021, (ii) We have, 95 x 96 = (100 – 5) (100 – 4) Thus, the required remainder is -π3 + 3π2 – 3π+1. = (2a – b) (2a – b) (2a – b), (iii) 27 – 125a3 – 135a + 225a2 ⇒ x3 + y3 + z3 = 3xyz ⇒ 3x = 2 (ii) The given polynomial is 4- y2. Extra questions for class 9 maths chapter 1 with solution. (i) (- 12)3 + (7)3 + (5)3 (ii) (x+8) (x -10) Chapter-2 Chapter-10 Sol. (i) Given that p(y) = y2 – y + 1. Middle school is one of the most crucial periods a student undergoes in the course of their schooling years. NCERT Solutions for Class 9 Maths Exercise 9.2 book solutions are available in PDF format for free download. Thus, zero of x + 5 is -5. (iv) 2y3 + y2 – 2y – 1 Solution: Exercise 13.2 Solution. (i) Volume 3x2 – 12x (iv) p (x) = 3x – 2 Since, p(x) = 0 => ax = 0 => x-0 Solutions to all NCERT Exercise Questions and Examples of Chapter 2 Class 9 Polynomials are provided free at Teachoo. (i) p(x)=x+5 (i) x3+x2+x +1 = (4m – 7n)[(4m)2 + (4m)(7n) + (7n)2] NCERT solutions for session 2019-20 is now available to download in PDF form. (x + a) (x + b) = x2 + (a + b) x + ab Solution: Question 4. We have, (x + 8) (x – 10) = x2 + [8 + (-10)] x + (8) (- 10) NCERT Solutions Class 9 Maths Chapter 2 Polynomials. (iii) \(\frac { \pi }{ 2 }\) x2 + x = 1 – 3 + 3 – 1 + 1 = 1 Chapter 9 Trigonometric Ratios – Mathematics Easter Holiday Assignment Chapter 9.2 Finding Trigonometric Ratios by Constructing Right-Angled Triangles Key Points If one of the trigonometric ratios of an acute angle θ = 4 1 cos e.g. (iv) p (x) = (x-1) (x+1) You have these advantages of browsing notes from our website. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx, (i) (x + 2y + 4z)2 Solution: (ii) We have, p(x) = x – 5. Question 1. (iv) We have, p(x) = 3x – 2. So, it is a linear polynomial. Class 9 maths printable worksheets, online practice and online tests. Find the value of k, if x – 1 is a factor of p (x) in each of the following cases Verify that Extra questions along with questions of NCERT book complete the topic . = 4k[(3y + 5) x (y – 1)] Then, x + y + z = -12 + 7 + 5 = 0 Using identity, = (2y -1)2 Solution: Solution: (i) p (x) = x2 + x + k Thus, x3 – 2x2 – x + 2 = (x – 1)(x + 1)(x – 2), (ii) We have, x3 – 3x2 – 9x – 5 = 10 – 16 + 3 = -3 Factorise So, it is a cubic polynomial. Here on AglaSem Schools, you can access to NCERT Book Solutions in free pdf for Maths for Class 9 so that you can refer them as and when required. = 0 + 0 + 0 + 1 = 1 which is not a whole number. Thus, zero of 3x – 2 is \(\frac { 2 }{ 3 }\). So, it is a quadratic polynomial. Let x = -12, y = 7 and z = 5. because each exponent of x is a whole number. = 10000 + (10) x 100 + 21 Teachoo provides the best content available! (iii) (998)3 Hindi Medium and English Medium both are available to free download. ⇒ p (-1) ≠ 0 = (3x + y)(3x + y), (ii) We have, 4y2 – 4y + 12 ⇒ (x – y)[(x – y)2 + 3xy)] = x3 – y3 ⇒ P (-1) ≠ 1 Volume of a cuboid = (Length) x (Breadth) x (Height) Note: Important questions have also been marked for your reference. There is plenty to learn in this chapter about the definition and examples of polynomials, coefficient, degrees, and terms in a polynomial. (i) 10 (ii) 17 (iii)2+ 2 2. x3 – y3 = (x – y)(x2 + xy + y2) If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1, drop a comment below and we will get back to you at the earliest. Thus, the required remainder = \(\frac { 27 }{ 8 }\). = (2x + 1)(x + 3) We have, 64m3 – 343n3 = (4m)3 – (7n)3 ∴ p (-1)= (-1)4 + 3 (-1)3 + 3 (-1)2 + (- 1) + 1 (iii) 5t – √7 = – π3 + 3π2 – 3π +1 (i) 4x2 – 3x + 7 (iv) 3x2 – x – 4 So, (x+ 1) is a factor of x3 + x2 + x + 1. (iii) x = 2 Thus, x3 – 3x2 – 9x – 5 = (x + 1)(x – 5)(x +1), (iii) We have, x3 + 13x2 + 32x + 20 ⇒ k = √2 -1, (iv) Here, p(x) = kx2 – 3x + k (i) We have, x3 – 2x2 – x + 2 ∴ P(-1) = (-1)4 + (-1)3 + (-1)2 + (-1)+1 = (2a)3 – (b)3 – 3(2a)(b)(2a – b) These 9th class math notes notes contain theory of each and every chapter, solutions to every exercise and review exercises which are great for reviewing giant exercises. = 1000000 + 8 + 60000 + 1200 = 1061208, (iii) We have, 998 = 1000 – 2 The zero of x + 1 is -1. = ( 100)2 + [(- 5) + (- 4)] 100 + (- 5 x – 4) These expert faculties solve and provide the NCERT Solution for class 9 so that it would help students to solve the problems comfortably. [Using a3 + b3 + 3 ab(a + b) = (a + b)3] Since, p(x) = 0 (i) We have 4x2 – 3x + 7 = 4x2 – 3x + 7x0 ∴ 993 = (100 – 1)3 = (3x + y + z)[(3x)3 + y3 + z3 – (3x × y) – (y × 2) – (z × 3x)] (ii) (2x – y + z)2 So, it is a linear polynomial. Factorise the following using appropriate identities (i) 103 x 107 Download NCERT Solutions for Class 9 Maths in Hindi Medium for CBSE Board, UP Board (High School), MP Board, Gujrat Board and other board’s students who are following NCERT Books. ∴ p(-2) = (-2)3 + 3(-2)2+ 3(-2) + 1 ⇒ x = \(\frac { -5 }{ 2 }\) (iii) P (x) = x3 Represent the following irrational numbers on number line. Area of a rectangle = (Length) x (Breadth) (ii) We have, 12ky2 + 8ky – 20k On signing up you are confirming that you have read and agree to = (x + 1)(x + 2)(x + 10) (ii) A monomial of degree 100 can be √2y100. [Using (x + a)(x + b) = x2 + (a + b)x + ab] Solution: Find the value of the polynomial 5x – 4x2 + 3 at Chapter-1 Chapter-9 Sol. Since, p(2) = 0, so, x = 2 is also a zero of (x + 1)(x – 2). Check whether 7 + 3x is a factor of 3x3+7x. GoyalAssignments.com provides Free Downloads of Study materials (Assignments, Model Test Paper, Sample Paper, Previous Paper) of all subjects for CBSE Class 9 & 10 students. Factorise 27x3 +y3 +z3 -9xyz. ∴ (28)3 + (-15)3 + (-13)3 = 3(28)(-15)(-13) (iv) 64a3 -27b3 -144a2b + 108ab2 Since, p(x) = 0 ⇒ x – 5 = 0 ⇒ x = -5 = (2a)3 + (b)3 + 6ab(2a + b) ∴ The possible dimensions of the cuboid are 3, x and (x – 4). Also, p( 2) = (2 + 1)(2 – 2) = (3)(0) = 0 Click on exercise or topic link below to get started. Answers to each and every question is explained in an easy to understand way, with videos of all the questions. = -8 + 12 – 6 + 1 Solution: NCERT Solutions Class 9 Maths Chapter 2 Polynomials are worked out by the experts of Vedantu to meet the long-standing demand of CBSE students preparing for Board and other competitive Exams. Write the coefficients of x2 in each of the following (iv) (y2+ \(\frac { 3 }{ 2 }\)) (y2– \(\frac { 3 }{ 2 }\)) Thus, 12x2 -7x + 3 = (2x – 1) (x + 3), (ii) We have, 2x2 + 7x + 3 = 2x2 + x + 6x + 3 Solution: (iv) p (x) = (x + 1) (x – 2), x = – 1,2 = x2(x + 1) + 12x(x +1) + 20(x + 1) (ii) Let p (x) = x4 + x3 + x2 + x + 1 (iii) p (x) = kx2 – √2 x + 1 (iii) We have, = x3 – 4x2 + x + 6 and g (x) = x – 3 (iv) Let p (x) = x3 – x2 – (2 + √2) x + √2 (ii) p (x) = x – 5 These assignments will be available in updated form along with new assignments and chapter wise tests with solutions. NCERT Exemplar Class 9 Maths is very important resource for students preparing for IX Board Examination.Here we have provided NCERT Exemplar Problems Solutions along with NCERT Exemplar Problems Class 9. Write the following cubes in expanded form = (4m – 7n)(16m2 + 28mn + 49n2), Question 11. = (3x -1) (4x -1) = (3x + y + z)(9x2 + y2 + z2 – 3xy – yz – 3zx). Let x = 28, y = -15 and z = -13. ⇒ 3x = 0 ⇒ x = 0 (ii) The degree of x – x3 is 3. (viii) We have, p(x) = 2x + 1 which is not a whole number. Classify the following as linear, quadratic and cubic polynomials. All answers are solved step by step with videos of every question.Topics includeChapter 1 Number systems- What are Rational, Irrational, Real numbers, Law of Exponents, Expressing numbers in p/q (i) The zero of x + 1 is -1. (v) (3 – 2x) (3 + 2x) (i) We have, (x+ 4) (x + 10) ∴ P(0) = (0)2 – 0 + 1 = 0 – 0 + 1 = 1 CBSE Worksheets for Class 9 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. = (x + 1)[x(x – 5) + 1(x – 5)] ∴ \(p(-\frac { 1 }{ 3 } )\quad =\quad 3(-\frac { 1 }{ 3 } )\quad +\quad 1\quad =\quad -1\quad +\quad 1\quad =\quad 0\) Solution: = (3 – 5a)3 Write the following numbers in p/q form (i) 2.015 (ii) 0.235 Ans (399 235 ' 198 999) 4. So, it is not a polynomial in one variable. (i) 8a3 +b3 +12a2b+6ab2 (iii) x4 + 3x3 + 3x2 + x + 1 Solution: = 3[-420] = -1260, (ii) We have, (28)3 + (-15)3 + (-13)3 Factorise (i) The degree of x2 + x is 2. [Using (a – b)3 = a3 – b3 – 3ab (a – b)] ⇒ p (-1) ≠ 0 [Using a2 – 2ab + b2 = (a- b)2] We know that if x + y + z = 0, then, x3 + y3 + z3 = 3xyz CLASS 9 IX Sample Papers X Sample Papers CLASS 8 CLASS 07 Class 06 ... Chapter - 2: Polynomials. Chapter-10 Chapter-3 Sol. (iii) The given polynomial is \(\frac { \pi }{ 2 } { x }^{ 2 }\) + x. All the chapterwise questions with solutions to help you to revise complete CBSE syllabus and score more marks in Your board examinations. ∴ p(-1) = 2(-1)3 + (-1)2 – 2(-1) – 1 = 3(5460) = 16380. Also, p(-1) = (-1)2 -1 = 1 – 1 = 0 3. We have, (3x + 4) (3x – 5) = (3x)2 + (4 – 5) x + (4) (- 5) = 8a3 – 27b3 – 18ab(2a – 3b) p(1) = (1)2 – 1 + 1 = 1 – 1 + 1 = 1 = 4 x k x (3y2 + 2y – 5) = k – √2 + 1 = 0 Question 15. = 4x2 + y2 + z2 – 4xy – 2yz + 4zx, (iii) (- 2x + 3y + 2z)2 = (- 2x)2 + (3y)2 + (2z)2 + 2 (- 2x) (3y)+ 2 (3y) (2z) + 2 (2z) (- 2x) ⇒ 2x = -5 NCERT Solutions for Class 9 Maths are a set of solutions in the form of chapter-wise solutions made specifically for Class 9th students.

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