Raffles Institution Y4 WS1 Polynomials and Identities

Page 1 of 19 RAFFLES INSTITUTION RAFFLES PROGRAMME 2023 YEAR 4 MATHEMATICS TOPIC 2: REMAINDER & FACTOR THEOREMS AND PARTIAL FRACTIONS (MATH 1) WORKSHEET 1 Name: ( ) Class: 4 ( ) Date: WORKSHEET 1: POLYNOMIALS AND IDENTITIES think! Add Math Textbook A Chapter 4 p.54 Blended Learning Online (SDL) Students to access HeyMath! Lesson Year 4 / Remainder and Factor Theorem / Polynomial Identities / Introduction [5:20] (1) INTRODUCTION TO POLYNOMIAL The table shows some examples of polynomials and non-polynomials in one variable. Polynomials Non-polynomials 2 43xx−+ 11x x+− 54322746 1x x x xx+ − + −+ 1 23xx −−+ 4 52 2xx− 3xx− 8 3 24 12 xxx−− KEY UNDERSTANDING(S) Students will understand that  A polynomial can be written as LEARNER OUTCOMES At the end of this worksheet, students will be able to  Define a polynomial  Write a polynomial in the form  Distinguish between identities and equations.  Use long division to divide polynomials

Page 2 of 19 Compare the powers of x in polynomials with those in non-polynomials. What do you notice? Why is the number ‘8’ a polynomial? (2) DEFINITIONS A polynomial in x is an algebraic expression consisting of terms with non -negative integral powers of x only. NOTE: 1. 12 2 1 2 2 10, , , ... , , , nn n nn nax a x a x ax ax a−− −− are known as the terms of the polynomial. 1 2 210, , , ... , , , nn naa a aaa−− are called the coefficients of the polynomial. 0a is called the constant term. 2. The degree of a polynomial in x is the highest power of x that occurs in the polynomial. 3. Consider the polynomial 325 7 46xxx+ −+ . 35x is called the leading term as it contains the highest power of x . The coefficient of the leading term is called the leading coefficient. By convention, we usually arrange the terms of a polynomial in descending powers of the variable. 4. Commonly used notations for polynomials in x include P( )x , Q( )x , f( )x and g( )x . 5. P( )a is the value of P( )x when xa= . For example, to find the value of the polynomial 32P( ) 5 7 4 6xxxx= + −+ when 3x= , we substitute 3x= into P( )x : 32P(3) 5(3) 7(3) 4(3) 6 192 = + −+ = The general form of a polynomial in is , where the index is a non -negative integer and the coefficients are real numbers.

Page 3 of 19 6. Polynomials can be classified according to their degree and the number of terms. Polynomial Degree Name by degree No. of terms Name by no. of terms 8 7 11x−− 2 43xx−+ 3212 5xxx− + −+ 4 52 2xx− 54322746 1x x x xx+ − + −+ EG 1 Which of the following are polynomials? (a) 1x x+ (b) ( ) 3 21 9x−− (c) ( ) 2 5ex − (d) 12xx+− (e) 422 53 1x y xy y x− + +− (f) 2lg 3xx+ EG 2 Given that 42P( ) 2 3 7x xx x= −+− is a polynomial in x , determine the following: (a) 4Coefficient of x = _____