Research and publish the best content. Jul 6, 2019 - RD Sharma Class 9 Solutions Chapter 6 Factorisation of Polynomials Ex 6.2 These Solutions are part of RD Sharma Class 9 Solutions. Solution: in (ii) is 0 as there is no term of x2 i.e. Your best online resource for Class 9 Maths – We have designed comprehensive content covering all chapters in an elaborate and easy to understand language. Write the coefficient of x2 in each of the following: Which of the following expressions are polynomials in one variable and which are not? The class will be conducted in Hindi and the notes will be provided in English RD Sharma class 10 maths solutions chapter 2 is provided herewith the latest updated solutions. RD Sharma. The section teaches you the steps to factor a polynomial. Let x be a variable, n be a positive integer and a0, a1, a2,…., an be constants. In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division : (1 – 8), Question 1: f(x) = x3 + 4x2 – 3x + 10, g(x) = x + 4, f(-4) = (-4)3 + 4(-4)2 – 3(-4) + 10 = -64 + 64 + 12 + 10 = 22, Question 2: f(x) = 4x4 – 3x3 – 2x2 + x – 7, g(x) = x – 1, f(1) = 4(1)4 – 3(1)3 – 2(1)2 + (1) – 7 = 4 – 3 – 2 + 1 – 7 = -7, Question 3: f(x) = 2x4 – 6X3 + 2x2 – x + 2, g(x) = x + 2, f(x) = 2x4 – 6X3 + 2x2 – x + 2, g(x) = x + 2, f(-2) = 2(-2)4 – 6(-2)3 + 2(-2)2 – (-2) + 2 = 32 + 48 + 8 + 2 + 2 = 92, Question 4: f(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1, f(x) = 4x3 – 12x2 + 14x – 3, g(x) = 2x – 1, f(1/2) = 4(1/2)3 – 12(1/2)2 + 14(1/2) – 3 = ½ – 3 + 7 – 3 = 3/2, Question 5: f(x) = x3 – 6x2 + 2x – 4, g(x) = 1 – 2x, f(1/2) = (1/2)3 – 6(1/2)2 + 2(1/2) – 4 = 1 + 1/8 – 4 – 3/2 = -35/8, Question 6: f(x) = x4 – 3x2 + 4, g(x) = x – 2, f(2) = (2)4 – 3(2)2 + 4 = 16 – 12 + 4 = 8, Question 7: f(x) = 9x3 – 3x2 + x – 5, g(x) = x – 2/3, f(2/3) = 9(2/3)3 – 3(2/3)2 + (2/3) – 5 = 8/3 – 4/3 + 2/3 – 5/1 = -3, In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1-7), Question 1: f(x) = x3 – 6x2 + 11x – 6; g(x) = x – 3. Question 3. NCERT Solutions for Class 12 Maths; NCERT Solutions for Class 12 Physics All Chapter 6 - Factorization of Polynomials Ex 6.1 Questions with Solutions for RD Sharma Class 9 Maths to help you to revise complete Syllabus and Score More marks. (ii) x2 – 2tx + 7t2 – x + t (ii) Degree of the polynomial 12 – x + 2x 3 is 3, since the term x 3 is highest (iii) Degree of the polynomial 5y – √2 is 1, since the term 5y only has the variable. The complete syllabus has been categorised based on chapters. 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To download our free pdf of Chapter 2 - Polynomials RD Sharma Solutions for Class 10 to help you to score more marks in your board exams and as well as competitive exams. Let x be a variable, n be a positive integer and a 0, a 1, a 2,…., a n be constants. Give one example each of a binomial of degree 35 and of a monomial of degree 100. (ii) 3x – 2 Learn CBSE. We have provided RD Sharma Solutions for class 9 Maths to help the students to understand the main concepts and the tough questions. Then anxn + a(n-1)x(n-1) + a(n-2)x(n-2) + ….+ a1 x + a0 is known as polynomial in variable x. RD Sharma Solutions Class 9 Maths (v) t2+ 1: It is a quadratic polynomial as its degree is 2. (ii) 3x – 2 : It is a linear polynomial as its degree is 1. Free PDF download of RD Sharma Solutions for Class 9 Maths Chapter 1 - Number System solved by Expert Mathematics Teachers on Vedantu.com. This will clear students doubts about any question and improve application skills while preparing for board exams. Class 9 RD Sharma Solutions - Chapter 14 Quadrilaterals- Exercise 14.1; Class 9 NCERT Solutions - Chapter 9 Areas of Parallelograms And Triangles - Exercise 9.1; Class 9 NCERT Solutions - Chapter 6 Lines And Angles - Exercise 6.3; Class 9 RD Sharma Solutions - Chapter 13 Linear Equation in Two Variable- Exercise 13.4 In the 6th chapter of Class 9 RD Sharma Solutions students will study important concepts on Factorization of Polynomials as listed below: Your email address will not be published. RS Aggarwal Solutions Class 9 Chapter 2 Polynomials NCERT Exemplar Class 9 Maths ¡s very important resource for students preparing for IX Board Examination. What is a polynomial? Find the value of the polynomial 5x – 4x2 + 3 at x = 2 and x = –1. Solution: RD Sharma Solutions Class 9 Factorisation of Polynomials Introduction Your best online resource for Class 9 Maths – We have designed comprehensive content covering all chapters in an elaborate and easy to understand language. (v) t2 + 1 We have prepared these solutions as per the the latest syllabus prescribed by the Central Board of Secondary Education (CBSE). Class 9 Maths Chapter 2 of the RD Sharma textbook has questions based on important topics like Integral Exponents of a Real Number, Laws of Integral Exponents, and Rational Exponents of a Real Number. In this Chapter 6 - Factorization of Polynomials, several exercise questions with solutions for RD Sharma Class 9 Maths are given to help the students and understand the concepts better. Trinomial: A polynomial containing three terms. Question 9. (ii) Degree of the polynomial 12 – x + 2x3 is 3 (v) Degree of the polynomial 0 is undefined. RD Sharma class 9 maths Solutions Factorization of Polynomials Chapter 6 Exercise 6.1 Q 1. Question 8: Show that (x – 2), (x + 3) and (x – 4) are factors of x3 – 3x2 – 10x + 24. f(2) = (2)3 – 3(2)2 – 10 x 2 + 24 = 8 – 12 – 20 + 24 = 32 – 32 = 0, f(-3) = (-3)3 – 3(-3)2 – 10 (-3) + 24 = -27 -27 + 30 + 24 = -54 + 54 = 0, f(4) = (4)3 – 3(4)2 – 10 x 4 + 24 = 64-48 -40 + 24 = 88 – 88 = 0, Hence (x – 2), (x + 3) and (x – 4) are the factors of f(x). Jun 20, 2018 - RD Sharma Class 9 Solutions Chapter 6 Factorisation of Polynomials Ex 6.1 These Solutions are part of RD Sharma Class 9 Solutions. Sharma Solutions for Class 9th Math MCQ The questions provided in RD Sharma (2019) Books are prepared in accordance with CBSE, thus holding higher chances of appearing on CBSE question papers. If g(x) is a factor of f(x), then the remainder will be zero that is g(x) = 0. R.D. Using factor theorem, factorize each of the following polynomials: Step 1: Find the factors of constant term, f(-2) = (−2)3 + 6(−2)2 + 11(−2) + 6 = -8 + 24 – 22 + 6 = 0, f(-3) = (−3)3 + 6(−3)2 + 11(−3) + 6 = -27 + 54 – 33 + 6 = 0, f(1) = (1)3 + 2(1)2 – 1 – 2 = 1 + 2 – 1 – 2 = 0, f(-1) = (-1)3 + 2(-1)2 – 1 – 2 = -1 + 2 + 1 – 2 = 0, f(-2) = (-2)3 + 2(-2)2 – (-2) – 2 = -8 + 8 + 2 – 2 = 0, f(2) = (2)3 + 2(2)2 – 2 – 2 = 8 + 8 – 2 – 2 = 12 ≠ 0, f(-1) = (-1)3 – 6(-1)2 + 3(-1) + 10 = 10 – 10 = 0, f(-2) = (-2)3 – 6(-2)2 + 3(-2) + 10 = -8 – 24 – 6 + 10 = -28, f(2) = (2)3 – 6(2)2 + 3(2) + 10 = 8 – 24 + 6 + 10 = 0, f(5) = (5)3 – 6(5)2 + 3(5) + 10 = 125 – 150 + 15 + 10 = 0, Therefore, (x + 1), (x – 2) and (x-5) are factors of f(x), f(1) = (1)4 – 7(1)3 + 9(1)2 + 7(1) – 10 = 1 – 7 + 9 + 7 -10 = 0, f(-1) = (-1)4 – 7(-1)3 + 9(-1)2 + 7(-1) – 10 = 1 + 7 + 9 – 7 -10 = 0, f(2) = (2)4 – 7(2)3 + 9(2)2 + 7(2) – 10 = 16 – 56 + 36 + 14 – 10 = 0, f(5) = (5)4 – 7(5)3 + 9(5)2 + 7(5) – 10 = 625 – 875 + 225 + 35 – 10 = 0, Therefore, (x – 1), (x + 1), (x – 2) and (x-5) are factors of f(x), Hence f(x) = (x – 1) (x + 1) (x – 2) (x-5), Factors of 12 are ±1, ±2, ±3, ±4, ±6, ±12, f(1) = (1)4 – 2(1)3 – 7(1)2 + 8(1) + 12 = 1 – 2 – 7 + 8 + 12 = 12, f(-1) = (-1)4 – 2(-1)3 – 7(-1)2 + 8(-1) + 12 = 1 + 2 – 7 – 8 + 12 = 0, f(-2) = (-2)4 – 2(-2)3 – 7(-2)2 + 8(-2) + 12 = 16 + 16 – 28 – 16 + 12 = 0, f(2) = (2)4 – 2(2)3 – 7(2)2 + 8(2) + 12 = 16 – 16 – 28 + 16 + 12 = 0, f(3) = (3)4 – 2(3)3 – 7(3)2 + 8(3) + 12 = 0, Therefore, (x + 1), (x + 2), (x – 2) and (x-3) are factors of f(x), Hence f(x) = (x + 1)(x + 2) (x – 2) (x-3), Factors of 24 are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, f(-1) = (-1)4 + 10(-1)3 + 35(-1)2 + 50(-1) + 24 = 1 – 10 + 35 – 50 + 24 = 0, Likewise, (x + 2),(x + 3),(x + 4) are also the factors of f(x), Hence f(x) = (x + 1) (x + 2)(x + 3)(x + 4), Factors of -45 are ±1, ±3, ±5, ±9, ±15, ±45, Here coefficient of x^4 is 2. If x+1 is a factor of x3 + a then f(-1) = 0. These RD Sharma Solutions class 9 helps students save considerable time when can be invested in clearing another subject topic. The questions asked in the textbooks may be easy or difficult. Question 3: Write the remainder when the polynomial f(x) = x3 + x2 – 3x + 2 is divided by x + 1. Practising the questions from the RD Sharma book is advantageous for the students as it gives them a brief description of the various questions from all the important topics. (iii) h(x) = -3x + $$\frac { 1 }{ 2 }$$ : It is a linear polynomial. Sharma Class 9 solutions we present here will help you lay a strong foundation of the basic Mathematics concepts that can help you ace the board exam as well as other competitive exams you are appearing for. Here you can freely download RD Sharma Solutions for class 9 Maths Book, We have listed all the chapters PDF’s. After completing this chapter of RD Sharma, students will be able to define and solve the geometrical representation of linear and quadratic polynomials, the geometric meaning of their zeros and relationship between the zeros and of a polynomial. It provides answers to the questions given in the textbook. Class 9 RD Sharma Solutions - Chapter 13 Linear Equation in Two Variable- Exercise 13.4; Class 9 RD Sharma Solutions - Chapter 9 Triangles and its Angles- Exercise 9.2; Class 9 NCERT Solutions - Chapter 1 Number System - Exercise 1.2; Class 9 RD Sharma Solutions - Chapter 16 Circles - … Free PDF download of RD Sharma Class 9 Solutions Chapter 6 - Factorization of Polynomials Exercise 6.1 solved by Expert Mathematics Teachers on Vedantu.com. (iii) 2x + x2: It is a quadratic polynomial. Question 6. Class 9 RD Sharma Textbook Solutions Chapter 6 - Factorization of Polynomials. All the Solutions available here are latest. It is that value of y that makes the polynomial equal to zero. If x + a is a factor of x 4 – a 2 x 2 + 3x – 6a, then a = (a) 0 (b) … We have provided step by step solutions for all exercise questions given in the pdf of Class 9 RD Sharma Chapter 6 - Factorization of … Do tests many times and check your score and download certificate.Doing mock online tests will help you to check your understanding and identify areas of improvement. (ii) y2 + 2$$\sqrt { 3 }$$ are polynomial is one variable. Class 9 RD Sharma Solutions All Chapters. Rd Sharma (2017) Solutions for Class 9 Math Chapter 6 Factorization Of Polynomials are provided here with simple step-by-step explanations. (iii) Degree of the polynomial 5y – $$\sqrt { 2 }$$is 1 RD Sharma book is designed as per the latest CBSE syllabus and topics covered in NCERT book. Page No 49: Question 15: Give possible expressions for the length and breadth of each of thefollowing rectangles, in which their areas are given: Answer: Area = Length × Breadth. Here we have given RD Sharma Class 9 Solutions Chapter 6 Factorisa… MCQ Questions for Class 9 Maths with Answers were prepared based on the latest exam pattern. RD Sharma Solutions for Class 9 Mathematics CBSE, 5 Factorisation of Algebraic Expressions. All the solutions of Factorisation of Polynomials - Mathematics explained in detail by experts to help students prepare for their CBSE exams. If you have any doubts, please comment below. So possible rational roots of f(x) are, ±1, ±3, ±5, ±9, ±15, ±45, ±1/2,±3/2,±5/2,±9/2,±15/2,±45/2, f(1) = 2(1)4 – 7(1)3 – 13(1)2 + 63(1) – 45 = 2 – 7 – 13 + 63 – 45 = 0, f(3) = 2(3)4 – 7(3)3 – 13(3)2 + 63(3) – 45 = = 162 – 189 – 117 + 189 – 45= 0, Now, we are available with 2 factors of f(x), (x – 1) and (x – 3), Question 1: Define zero or root of a polynomial. Monomial: A polynomial containing only one term. This chapter goes deep into the topic of identities, identity for the square of a … NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. Solution: Solution: (iv) xy +yz + zx : It is a polynomial in 3 variables in x, y and. RD Sharma Class 9 Maths Solutions for Chapter 6 – Factorization of Polynomials includes all the questions provided in the textbooks prepared by Mathematics expert teachers from Mathongo.com. Question 4: Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: (i) x + x2 + 4: It is a quadratic polynomial as its degree is 2. Also, step by step solutions are provided for questions along with relevant tips and tricks. in (i) is 7 Access full series of free online mock tests with answers from Polynomials Class 9. The expression given for the area of the rectangle has to be factorised. The book has tons of problems that help students to build a strong foundation in math. In this chapter, students will learn various terms such as polynomial, degree of polynomial, factors, multiples and zeros of a polynomial. RD Sharma Solutions for Class 10 Mathematics CBSE, 2 Polynomials. (iv) 3y It is a linear polynomial. RD Sharma covers questions from different difficulty level, from the simple questions to the advanced questions, where students get to know all the important questions. RD Sharma Class 9 maths textbook is in accordance with the latest syllabus prescribed by CBSE. The section teaches you the steps to factor a polynomial. Expand : (i) (y – √3) 2 (ii) (x – 2y – 3z) 2 Solution: (i) (y – √3) 2 = y 2-2 × y × √3 + (√3) 2 = y 2 – 2√3 y + 3 (x – 2y – 3z) 2 = x 2 + 1 – 2y) 2 + (-3z) 2 + 2 × x × (-2y) + 2 × (-2y) × (-3z) + 2 × (-3z) × x = x 2 + 4y 2 + 9z 2 – 4xy + 12yz – 6zx. Hence (x + 4), (x – 3), (x – 7) are the factors of f(x). The chapter deals with polynomials and while this chapter can sometimes be a little confusing, the RD Sharma solutions for math that we have given here has been crafted in such a way to help students understand the concepts easily and clearly. p(1) = 13 – 6(1)2 + 11x 1 – 6 = 1 – 6 + 11 – 6 = 0, p(2) = 23 – 6(2)2 + 11×2 – 6 = 8 – 24 + 22 – 6 = 0, p(3) = 33 – 6(3)2 + 11×3 – 6 = 27 – 54 + 33 – 6 = 0. In this chapter, students will learn various terms such as polynomial, degree of polynomial, factors, multiples and zeros of a polynomial. Students doubts about any question in the most popular study materials with the latest CBSE syllabus and More. Exemplar Problems Solutions along with NCERT Exemplar Problems Solutions along with NCERT Problems... Provided Polynomials Class 9 Maths to help students understand the concept very well 8, 9,,! Classify the following expressions are Polynomials in one-variable, two-variables etc for questions along with tips... 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