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Chapter 8.4 POLYNOMIALS Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems Students will know the terms for polynomials. Students will know how to arrange polynomials in ascending and descending order. POLYNOMIALS Monomial – a number, a variable or a number and variable multiplied together. Ex: 3, x2, or 5x Polynomial – a monomial or sum of monomials. Ex: 2, x, 3x2 + 2x Binomial – the sum or difference of two monomials. Ex: 3x2 + 2x Trinomial – The sum or difference of three monomials. Ex: 3x2 + 2x – 7 *Numbers that are being divided are not monomials or any of these types of problems. Ex: 2/x is not a monomial, polynomial, binomial, or trinomial! POLYNOMIALS Ascending order – increasing from the smallest to the largest. Ex: 1, 3, 4, 6, 7 Descending order – Decreasing from the largest to the smallest. Ex: 8, 5, 4, 2, 1 *When re-ordering a problem into ascending or descending order use the exponents (powers) of the variable to determine which goes first. POLYNOMIALS Example 1: Arrange the terms or each polynomial so that the powers of x are in ascending order: x4 – x2 + 5x3 Answer: – x2 + 5x3 + x4 POLYNOMIALS 1. Write in ascending order: 8, 16, 2, 6, 21, 0 2. Write in ascending order: 1. 2x3 + 3x5 + 4x 2. 5x2 – 6x4 + 2x3 3. 23x8 + 14x5 – 34x2 POLYNOMIALS Example 2: Arrange the terms or each polynomial so that the powers of x are in ascending order: 8x3y – y2 + 6x2y + xy2 Answer: – y2 + xy2 + 6x2y + 8x3y POLYNOMIALS Put the following in ascending order according to the x value. 1. 2x2y3 + 3x3y6 + 4xy 2. 5x7y5 – 2x2y4 + 7x4y2 3. 12x4y2 – y5 + 3x + 8x6y3 POLYNOMIALS Example 3: Arrange the terms or each polynomial so that the powers of x are in descending order: x4 – x2 + 5x3 Answer: x4 + 5x3 – x2 POLYNOMIALS 1. Write in descending order: 8, 16, 2, 6, 21, 0 2. Write in descending order: 1. 2x3 + 3x5 + 4x 2. 5x2 – 6x4 + 2x3 3. 23x8 + 14x5 – 34x2 POLYNOMIALS Example 4: Arrange the terms or each polynomial so that the powers of x are in ascending order: 8x3y – y2 + 6x2y + xy2 Answer: 8x3y + 6x2y + xy2 – y2 POLYNOMIALS Put these in descending order according to the X value 1. 2x2y3 + 3x3y6 + 4xy 2. 5x7y5 – 2x2y4 + 7x4y2 3. 12x4y2 – y5 + 3x + 8x6y3 POLYNOMIALS 1. 2. 3. 4. True or False: 3x2 is a monomial. T or F: 5x – 2 is a trinomial. Arrange in ascending order: 3x – 7 + 5x2 Arrange in descending order by the powers of x: a) 2x + 3x2 – 7 b) 7xy2 – 5x3y + 2y4