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Chapter 8.4

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P OLYNOMIALS 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.

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P OLYNOMIALS Monomial – a number, a variable or a number and variable multiplied together. Ex: 3, x 2, or 5x Polynomial – a monomial or sum of monomials. Ex: 2, x, 3x 2 + 2x Binomial – the sum or difference of two monomials. Ex: 3x 2 + 2x Trinomial – The sum or difference of three monomials. Ex: 3x 2 + 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!

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P OLYNOMIALS 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.

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P OLYNOMIALS Example 1: Arrange the terms or each polynomial so that the powers of x are in ascending order: x 4 – x 2 + 5x 3 Answer: – x 2 + 5x 3 + x 4

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P OLYNOMIALS 1. Write in ascending order: 8, 16, 2, 6, 21, 0 2. Write in ascending order: 1. 2x 3 + 3x 5 + 4x 2. 5x 2 – 6x 4 + 2x x x 5 – 34x 2

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P OLYNOMIALS Example 2: Arrange the terms or each polynomial so that the powers of x are in ascending order: 8x 3 y – y 2 + 6x 2 y + xy 2 Answer: – y 2 + xy 2 + 6x 2 y + 8x 3 y

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P OLYNOMIALS Put the following in ascending order according to the x value. 1. 2x 2 y 3 + 3x 3 y 6 + 4xy 2. 5x 7 y 5 – 2x 2 y 4 + 7x 4 y x 4 y 2 – y 5 + 3x + 8x 6 y 3

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P OLYNOMIALS Example 3: Arrange the terms or each polynomial so that the powers of x are in descending order: x 4 – x 2 + 5x 3 Answer: x 4 + 5x 3 – x 2

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P OLYNOMIALS 1. Write in descending order: 8, 16, 2, 6, 21, 0 2. Write in descending order: 1. 2x 3 + 3x 5 + 4x 2. 5x 2 – 6x 4 + 2x x x 5 – 34x 2

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P OLYNOMIALS Example 4: Arrange the terms or each polynomial so that the powers of x are in ascending order: 8x 3 y – y 2 + 6x 2 y + xy 2 Answer: 8x 3 y + 6x 2 y + xy 2 – y 2

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P OLYNOMIALS Put these in descending order according to the X value 1. 2x 2 y 3 + 3x 3 y 6 + 4xy 2. 5x 7 y 5 – 2x 2 y 4 + 7x 4 y x 4 y 2 – y 5 + 3x + 8x 6 y 3

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P OLYNOMIALS 1. True or False: 3x 2 is a monomial. 2. T or F: 5x – 2 is a trinomial. 3. Arrange in ascending order: 3x – 7 + 5x 2 4. Arrange in descending order by the powers of x: a) 2x + 3x 2 – 7 b) 7xy 2 – 5x 3 y + 2y 4

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