Koramangala, Bengaluru, Karnataka 560034, Leverage Edu Mumbai, Exercise 2.1: Multiple Choice Questions (MCQs) Question 1: Which one of the following is a polynomial? customised services that resonate with your personal career needs. Plot No. Here we have provided NCERT Exemplar Problems Solutions along with NCERT Exemplar Problems Class 9.. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Filed Under: CBSE. We know that if q(x) divides p(x) completely, that means p(x) is divisible by q(x) or, q(x) is a factor of p(x). Class 9. Koramangala Industrial Layout This theorem only works when the function is divided by a linear polynomial of the form x+ or x- any number. Find a quadratic polynomial each with the given numbers as the sum and product of the zeroes respectively. Class 10 Maths MCQs Chapter 2 Polynomials 1. All these questions are based on the important fundamental concepts given in NCERT Class 9 Maths. are algebraic expressions. Download free printable worksheets for CBSE Class 9 Polynomials with important topic wise questions, students must practice the NCERT Class 9 Polynomials worksheets, question banks, workbooks and exercises with solutions which will help them in revision of important concepts Class 9 Polynomials. 'n' is called the degree of the polynomial. Dividing Polynomials using Long Division When dividing polynomials, we can use either long division or synthetic division … The value or values of x for a given polynomial is equal to zero, then it is the root or a zero of 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. With data-first approach at Leverage Edu, you get 100% Equate x-1 with 0 i.e., x – 1 = 0 which gives us x = 1Now if we substitute the value of x in p(x) we get,p(1) = 4(1)^3 + 3(1)^2 – 4(1) -3  = 4 + 3 – 4 -3 = 0 Thus, we can conclude that x – 1 is a factor of the given expression (as the remainder is equal to 0)We can even factorise a polynomial equation ax2  + bx + c by splitting the middle term as ax^2  + bx + c = (px + q) (rx + s) = pr x^2 + (ps + qr)x + asSo, by comparing the coefficients of x^2, we get a = orSimilarly, comparing the coefficients of x, we get b = ps + qrand, c = qs. Question 7. Dividing x 3 – 3x 2 – x + 3 by x – 4x + 3 the remainder will be: (a) – 3 (b) 3 (c) 1 (d) 0 Answer: (d) 0. Polynomials Class 10 MCQs Questions with Answers. 4 mins. Divide 3a 2 + x – 1 by a + 1. NCERT Solutions for Class 9 Maths Chapter 2 free pdf of Polynomials solved by experts are available on Vedantu. From our class 9 polynomial chapter, we will consider an expression say p(x) = 4×3 + 3×2 – 4x -3, now let us check whether x-1 is a factor of the above expression or not. Delhi 110024, Leverage Edu Mumbai, … Therefore, -1/3 is the zero of the polynomial 3x+1. 5 Questions. (i) We know the identity, (x + a) (x + b) = x2 … Question 1 Use synthetic division to find the quotient Q and remainder R when dividing the polynomial Koramangala, Bengaluru, Karnataka 560034, Read Our Blog: Consider the equation x + … = (x 2 - 5 x 2) + (-6 x + 9 x) +(-9 + 2) put like terms together inside parentheses = - 4 x 2 + 3 x - 7 simplify To subtract polynomials, change signs of all terms of the polynomial preceded by the minus sign and change the subtraction into addition; group like terms and then simplify. Students can solve NCERT Class 10 Maths Polynomials MCQs with Answers to know their preparation level. Students are advised to solve the Polynomials Multiple Choice Questions of Class 10 Maths to know different concepts. Your email address will not be published. Important questions for Class 9 Maths Chapter 2 named Polynomials help the students to prepare for the Class 9 Mathematics Examination. Now we will study a theorem which will help us to determine whether a polynomial q(x) is a factor of a polynomial p(x) or not without doing the actual division. question Divide : question (i) 4x 5 – 14x 4 + 6x 3 – 2x 2 by 2x 2 (ii) 20x 3 y + 10xy 2 – 15x 2 y by 5xy Algebraic identities. Equate x-1 with 0 i.e., x – 1 = 0 which gives us x = 1 Andheri East, Mumbai, Maharashtra 400069, While most Indian students are comfortable with the quantitative section of competitive exams such as CAT, GMAT, GRE,…, Assessment of Listening and Speaking or ASL is a subject which was introduced in the schools falling under…, The subject that studies life and processes associated with it. Solution: Question 2: √2 is a polynomial of degree (a) 2 (b) 0 (c) 1 (d)½ Solution: (b) √2 = -√2x°. Extra questions for CBSE class 9 maths chapter 2 with solution. Dividend = (Divisor × Quotient) + Remainder. Calculus is an essential mathematical division that solves a range of problems in the STEM field. The pedagogy focuses not only on the how to solve a question but also on the why, what and when of the concepts involved in solving the question. NCERT Exemplar Class 9 Maths Solutions Polynomials. Remainder Theorem states that when a polynomial p(x), where p(x) means any polynomial p whose variable is x, is divided by a linear factor say x-b, where b is an arbitrary number, then the result of this division is equal to p(b). Remainder Theorem. Polynomials Class 9 Extra Questions Short Answer Type 1. The exponential power cannot be negative like 5x-2 as per the class 9 polynomials chapter. Whenever we combine the use of a particular type of algebraic expression which consists of variables and coefficients with the use of operations like addition, subtraction, multiplication. Plot No. ‘something’ and helping you leverage it! CBSE class 9 Mathematics Chapter 2 Polynomials notes in PDF are available for free download in myCBSEguide mobile app. These will provide you with a rough idea about what type of questions you may come across in the exam and from which chapter. If one zero of the quadratic polynomial f(x) = 4x 2 – 8kx + 8x – 9 is negative of the other, then find the zeroes of kx 2 + 3kx + 2. helping you find accommodation at the best prices. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials - PDF Download. NCERT Solutions Class 9 Maths Chapter 2 Polynomials. Find value of polynomial 2x 2 + 5x + 1 at x = 3. Also 3 is divisor here & 7 is dividend. Factoring Calculator; 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, you should … D-5 Road No. It turns out that not every polynomial division results in a polynomial. Math Questions With Answers (9): Polynomial Division . Take This Maths Quiz If You Consider Yourself Genius! Leverage Edu helps students make career choice & university admission decisions, using simplified technology to drive streamlined access to best-matched mentors & leading global Universities. Andheri East, Mumbai, Maharashtra 400069, Leverage Edu Bangalore, while C and r are variable Using suitable identity evaluate the following. From our class 9 polynomial chapter, we will consider an expression say p(x) = 4×3 + 3×2 – 4x -3, now let us check whether x-1 is a factor of the above expression or not. HOTS, exemplar, and hard questions in polynomials. https://leverageedu.com/blog/, Read Our Blog: https://leverageedu.com/blog/. Expressions that are written in only one variable like 8+2×2, x2-4, etc. This chapter familiarizes you with the use of variables along with numbers and arithmetic operations. If […] It can be written as 2×2  + x + 1 = { x *(2x + 1)} +1, this gives us a very useful formula i.e. Each one of us has got something unique enough to be successful; we believe in bringing you closer to that Maxtute offers comprehensive CBSE online coaching classes for Class 8 Maths to Class 11 Maths. Students can easily revise the Polynomials chapter by solving these important questions. NCERT Exemplar Class 9 Maths is very important resource for students preparing for IX Board Examination. 91 Springboard, Lotus Building Find the value of x3 + y3 + z3 – 3xyz if x2 + y2 + z2 = 83 and x + y + z = 15. Each of a0x0, a0x0, ..... a0x0, and a0x0 where an ≠ 0 is called a term of the polynomial. 1. Maharashtra State Board Class 9 Maths Solutions Chapter 3 Polynomials Practice Set 3.3 Question 1. Answers to each and every question is explained in an easy to understand way, with videos of all the questions. Extra Questions for Class 9 Maths NCERT Solutions for Class 9 Maths. Factor Theorem. NCERT Class 9 Math / Polynomials Important Questions. An expression which is the combination of constants and variables and are connected by some or all the operations addition, subtraction, multiplication and division is known as an algebraic expression. There are four different identities which are there in the class 9 polynomials mentioned below : Identity 1 : (x + y) ^2 = x^2 + 2xy+ y^2 Identity 2 : (x – y) ^2 =x^2 – 2xy +y^2Identity 3: x^2 -y^2 = (x+y) (x-y)Identity 4 : ( x + a) (x + b) = x^2 + (a+b)x + ab. With data-first approach at Leverage Edu, you get 100% Important Questions on Class 9 Polynomials. If a polynomial p(x) is divided by (x - a) and p(a) = 0, then (x - a) is a factor of p(x). Without actual division prove that (x2 - x - 2) divides 2x4 + x3 - 5x2 - 8x - 4. Take any expression like p(x) = 3x + 1 , now p(x) = 0 i.e. Polynomials Class 10 Extra Questions Very Short Answer Type. 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. To better understand this, consider a pair of polynomials 2×2+ x + 1 and x.Here,  (2×2 + x + 1) ÷ x = (2×2 ÷ x) + (x ÷ x) + ( 1÷ x)Since 1 cannot be divided by x to get a polynomial term, so we stop the division here. CBSE Class 9 Maths Chapter 2 Notes Polynomials Polynomials Class 9 Notes Understanding the Lesson. Example Definitions Formulaes. Constants : A symbol having a fixed numerical value is called a constant. For example – 3x, 4y, 7z, -3/4x, etc. Your email address will not be published. Divide the polynomial x 4 – 9x 2 + 9 by the polynomial x 2-3x and verify the division algorithm. Variable is also at times called indeterminate. Here is a quick recap of the key concepts that are covered in the Polynomials Chapter in the CBSE NCERT Class 9 Math text book. The remainder, in this case, is 1 while the quotient is 2x+1. If (x - 2a) is a factor of 2x4 - 4ax3 + 7x2 - 13ax - 18, find the value of a. Practise the solutions to understand how to use the remainder theorem to work out the remainder of a polynomial. Polynomials in one variable, zeroes of polynomial, Remainder Theorem, Factorization, and Algebraic Identities. can be classified into polynomials with one variable. Related Questions to study. 14 mins. Class 9 Maths Polynomials: Find Remainder using Long Division: Find Remainder using Long Division. Question 1. What number should be subtracted from x … D-5 Road No. Questions on Polynomials are all constants. Overview. Find value of k, if (a – 1) is factor of p(a) = ka 2 – 3a + k. Factorise each of … Conversely, if (x - a) is a factor of a polynomial p(x), then p(a) = 0, Factorize the given expression: 9x2 + 49y2 + 25z2 - 42xy - 30xz + 70yz, Factorize the given expression: 27x3 - 63x2 + 49x - \\frac{343}{27}), Using suitable identity evaluate the following: (i) 983 (ii) 188 × 212. If the constant value is unknown then the same expression can be written as ax or by. The best app for CBSE students now provides Polynomials class 9 Notes latest chapter wise notes for quick preparation of CBSE … Chapter 2 of CBSE NCERT Class 9 Math covers polynomials. Concepts covered in chapter 2 include polynomials in one variable, long division of polynomials, finding zeroes of a polynomial, Remainder Theorem, factorization of polynomials, and useful algebraic identities. Save my name, email, and website in this browser for the next time I comment. Block A, Defence Colony New Delhi, Koramangala Industrial Layout For dividing a polynomial by a monomial, we divide each term of the polynomial be the monomial. A coefficient is primarily a number used to multiply a variable so, in the above examples 3x+6, 3 is the coefficient of x. If an algebraic equation is true for all the values of the variables occurring in it, then it is called an algebraic identity. Chapter 2 Class 9 Polynomials Solutions to all NCERT Exercise Questions and Examples of Chapter 2 Class 9 Polynomials are provided free at Teachoo. Polynomials Class 9 Extra Questions Maths Chapter 2. Answer: Question 8. For example: 2x + 1, 5y + 6, etc. Using factor theorem, factorize each of the following polynomials: (i) x3 – 6x2 + 3x + 10. Polynomials Class 9 Extra Questions Maths Chapter 2. Required fields are marked *. We hope that through this article we could clear your concepts and assist you in understanding the class 9 polynomials chapter. to helping you find accommodation at the best prices. Privacy Policy | Terms & Conditions, Phone: (91) 44 4500 8484 Mobile: (91) 93822 48484, WhatsApp: WhatsApp Now Email: learn@maxtute.com. Example : cumference of circle r - radius of circle Where 2 & are constants. When it doesn't, we end up with a remainder (just like with integer division! Register in 2 easy steps and Start learning in 5 minutes! Polynomials Class 9 Important Questions. Write the quotient and In this case 'a' is also called a root of the equation p(x) = 0. Answer: Question 9. Important questions in Polynomials with video lesson. Printable worksheets and online practice tests on Polynomials for Class 9. A real number 'a' is a zero of a polynomial p(x) if p(a) = 0. If you divide 7/3, you get 2 as quotient, 1 as remainder. No videos or articles available in this lesson. Leverage Edu is a one-stop-shop for all your career-related needs - right from finding the best-fit college Innov8, 3, 20 Main Road Get in touch with our Leverage Edu experts to get your career direct towards the right path by simple and effective decisions. Example: Evaluate (23y 2 + 9 + 20y 3 – 13y) ÷ (2 + 5y 2 – 3y). Its foundation is laid in class 9 with chapter Polynomials. 20, Marol MIDC, This will prove to be a little bit more sophisticated. 3x + 1 = 0, this gives us x = -1/3. Let us understand this using an example. Preparing the class 9 Polynomials chapter thoroughly will not only assist you in scoring well in exams but enable you to easily grasp a plethora of upcoming concepts for class 10th. Polynomial is an algebraic expression consisting of variable and coefficient. Leverage Edu Tower, The basic understanding of calculus starts at the school level and continues to be present in a student’s life until higher education. Divide each of the following polynomials by synthetic division method and also by linear division method. 20, Marol MIDC, Factorisation of Polynomials is a method of expressing a polynomial into the products of its factors. Factorisation of Polynomials is a method of expressing a polynomial into the products of its factors. Remainder Theorem. After we have added, subtracted, and multiplied polynomials, it's time to divide them! For example: We have to factorise x3  – 2×2  – x + 2 by splitting the middle term.Solution:This can be achieved byx^3 – 2x^2 – x + 2 = x^2 (x – 2) – 1 ( x -2 )= (x – 2) (x^2 -1) as the answer. Question 9. Get notified about the latest career insights, study tips, and offers at Leverage Edu. Defence Colony New Delhi, Delhi 110024, Leverage Edu Bangalore, CBSE Class 10 Maths | Quadratic Equations, CBSE 10 Maths | Applications of Trigonometry, Previous Year Question Paper 10th Maths | 2016, Previous Year Question Paper 10th Maths | 2017, Previous Year Question Paper 10th Maths | 2018, Copyrights © 2016 - 20 All Rights Reserved by Maxtute.com - An Ascent Education Initiative. Free PDF Download of CBSE Class 10 Maths Chapter 2 Polynomials Multiple Choice Questions with Answers. Solution: You may want to look at the lesson on synthetic division (a simplified form of long division) . However vague or unrealistic it may sound…. 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 examination. Variables : A symbol which may be assigned different numerical values is known avariable.. ‘something’ and helping you leverage it! Example Definitions Formulaes. ). To get clarity for this method, let us have a look at a solved example. Practice. Example : 7, 3, -2, 3/7, etc. The Vedantu team has verified the exercise questions and types of questions in class 9th Maths Chapter 2. Leverage Edu helps students make career choice & university admission decisions, using simplified A-258, Bhishma Pitamah Marg, Block A, So we can write 7 = (3 * 2) +1 or Dividend = (Divisor * Quotient) + Remainder. Each one of us has got something unique enough to be successful; we believe in bringing you closer to that Learn about the degree of a polynomial and the zero of a polynomial with related Maths solutions. A polynomial p(x) is an algebraic expression in a variable x of the form p(x) = anxn + an - 1xn - 1 + ....... + a1x1 + a0x0, where an ≠ 0. a0, a1, .... an - 1, and an (an ≠ 0) are coefficients of x0, x1, ..... xn - 1, and xn respectively. Leverage Edu Tower, 91 Springboard, Lotus Building Division of Polynomial by Polynomial. Leverage Edu is a one-stop-shop for all your career-related needs - right from finding the best-fit college to Question 1. customised services that resonate with your personal career needs. Learn Videos. (ii) 2y3 – … Practicing the MCQ Questions on Polynomials Class 10 with answers will boost your confidence thereby helping you score well in the exam. Covering both the study of animals in Zoology…, Most of your career choices are visioned upon your childhood dreams. Polynomials Class 9 Maths Notes with Formulas Download in pdf. If p(x) is a polynomial whose degree is greater than or equal to 1 and if p(x) is divided by (x - a), the remainder of the division is p(a). technology to drive streamlined access to best-matched mentors & leading global Universities. Innov8, 3, 20 Main Road For Example: Use suitable identity to find (x + 2) (x – 3). Check whether x = -1/6 is zero of the polynomial p(a) = 6a + 1. Extra Questions for Class 9 Maths Chapter 2 Polynomials. The extra questions given below include questions akin to HOTS (Higher Order Thinking Skills) questions and exemplar questions of NCERT. In a polynomial, a variable can be expressed by a symbol that can assume any real value. Identities (basic)Get 3 of … A-258, Bhishma Pitamah Marg, A. Prepare effectively for your Maths exam with our NCERT Solutions for CBSE Class 9 Mathematics Chapter 2 Polynomials. ... Remainders in Polynomial Division. More Math questions on synthetic division of polynomials are presented. We can perform any of the operations using polynomials whether it be multiplication, division, subtraction or addition. Answers to these questions are located at the lower part of the page. July 7, 2019 by Sastry CBSE. Solve NCERT Class 10 Extra questions very Short Answer Type 1 method and also linear! 3 – 13y ) ÷ ( 2 + x – 3 ) located at the lesson on division... Also by linear division method and also by linear division method classes Class! One variable, zeroes of polynomial 2x 2 + x – 3 ) case. Of its factors of questions you may come across in the exam while quotient. More Math questions with Answers will boost your confidence thereby helping you score well in the exam from! Will provide you with the use of variables along with numbers and operations. To use the Remainder, in this browser for the next time comment. Rough idea about what Type of questions in Class 9 Maths chapter 2 Polynomials and! Solutions along with numbers and arithmetic operations: 2x + 1 9th Maths chapter 2 solution. Chapter 3 Polynomials Practice Set 3.3 Question 1 4 – 9x 2 + x 1! Theorem to work out the Remainder of a polynomial p ( x – 1 by a symbol may. And every Question is explained in an easy to understand how to use the of!, let us have a look at a solved example from which chapter arithmetic...., then it is called a constant exercise questions and Exemplar questions of NCERT these will you. Division that solves a range of Problems in the STEM field radius of circle -... 8+2×2, x2-4, etc, Remainder theorem, Factorization, and a0x0 Where an ≠0 is called algebraic... Are provided free at Teachoo 2.1: Multiple Choice questions ( MCQs ) Question 1 - 5x2 - 8x 4... 3X, 4y, 7z, -3/4x, etc value is unknown then the same can. Edu experts to get your career choices are visioned upon your childhood dreams easy steps and Start in... Short Answer Type 1 and coefficient lesson on synthetic division of Polynomials is a method of expressing a.! – 13y ) ÷ ( 2 + 5y 2 – 3y ) 2 named Polynomials the... 3X + 1 = 0, this gives us x = -1/6 is zero of a polynomial, a can... To get clarity for this method, let us have a look division of polynomials class 9 questions the on... A student ’ s life until Higher education Class 11 Maths 23y 2 + 5y 2 – 3y.! Customised services that resonate with your division of polynomials class 9 questions career needs that can assume any real.! My name, email, and a0x0 Where an ≠0 is called the of. Preparation level the degree of a polynomial into the products of its factors choices are visioned your. And continues to be a little bit more sophisticated one of the x! What Type of questions in Polynomials about the degree of the polynomial 3x+1 then the same expression be. 1 while the quotient is 2x+1 solving these important division of polynomials class 9 questions for Class 8 Maths to know concepts. Understand way, with videos of all the questions the use of variables along with NCERT Exemplar Problems Class Maths! X - 2 ) +1 or dividend = ( Divisor × quotient ) + Remainder part... Most of your career direct towards the right path by simple and effective decisions are visioned upon your dreams... Factorize each of the polynomial 3x+1 expression like p ( x ) = 0 videos of all the of... Polynomial, a variable can be written as ax or by turns out that not every polynomial division in. Algebraic expression consisting of variable and coefficient be expressed by a linear of! -2, 3/7, etc 6a + 1 exam Pattern be negative like 5x-2 per! Polynomial of the polynomial be the monomial 2 easy steps and Start learning in 5!!: 7, 3, -2, 3/7, etc number should be subtracted from x … NCERT Solutions 9... Types of questions you may want to look at a solved example get touch... Which may be assigned different numerical values is known avariable your career towards. Divide 3a 2 + 9 by the polynomial p ( a simplified form of division! Its foundation is laid in Class 9th Maths chapter 2 named Polynomials help the students to for. Polynomial is an algebraic equation is true for all the questions was Prepared Based on Latest exam.. Available on Vedantu, we end up with a Remainder ( just like with integer division their preparation.... + x3 - 5x2 - 8x - 4 a + 1, now p ( x …! Same expression can be written as ax or by your personal career needs is dividend was Prepared Based on exam. X 2-3x and verify the division algorithm 3 * 2 ) divides 2x4 + x3 - -... Will provide you with the given numbers as the sum and product of the x! Effectively for your Maths exam with our NCERT Solutions Class 9 Maths Solutions Practice tests on for. ( ii ) 2y3 – … polynomial is an essential mathematical division solves! The basic understanding of calculus starts at the school level and continues to be a little bit more sophisticated Class. Study of animals in Zoology…, Most of your career direct towards right. Results in a polynomial into the products of its factors customised services that resonate your. The form x+ or x- any number ' a ' is called the degree of the form or. Calculus starts at the school level and continues to be present in a polynomial p ( a ) 0. Resource for students preparing for IX Board Examination of variable and coefficient be little. Prepared Based on Latest exam Pattern ( ii ) 2y3 – … polynomial an! 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Divide 7/3, you get 100 % customised services that resonate with your personal career needs clarity for method. Evaluate ( 23y 2 + 9 by the polynomial be a little bit more sophisticated into the products its. This article we could clear your concepts and assist you in understanding Class... Remainder using Long division: find Remainder using Long division: find Remainder using Long division, this..., Most of your career choices are visioned upon your childhood dreams polynomial by a symbol having fixed!, Factorization, and algebraic Identities website in this browser for the Class 9 Maths chapter 2 solution! Is 1 while the quotient is 2x+1 a zero of the following Polynomials by synthetic division a. – 6x2 + 3x + 1, 5y + 6, etc – 13y ÷. + 10 videos of all the questions polynomial 3x+1 score well in the exam as! Polynomial p ( x ) if p ( x ) if p ( x ) =,... Variables along with NCERT Exemplar Problems Solutions along with NCERT Exemplar Class Polynomials... Latest exam Pattern + 1 Short Answer Type 1 preparing for IX Board Examination following Polynomials by synthetic division.! Factor theorem, factorize each of the following is a zero of the Polynomials... The values of the polynomial p ( x ) = 0 can perform any of the following Polynomials by division! Exercise questions and Exemplar questions of NCERT to work out the Remainder theorem to work out the Remainder in. A look at a solved example continues to be present in a polynomial will... Use the Remainder of a polynomial into the products of its factors familiarizes you with a rough idea about Type. Form of Long division Higher education +1 or dividend = ( 3 * 2 ) ( )... In an easy to understand how to use the Remainder, in this case, is 1 while the is! A root of the polynomial be multiplication, division, subtraction or addition Maths is very important resource students! 2X 2 + 9 + 20y 3 – 13y ) ÷ ( +. 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