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Polynomials Chapter 8.4

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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.

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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!

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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.

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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

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**Your Turn! Polynomials Write in ascending order: 8, 16, 2, 6, 21, 0**

2x3 + 3x5 + 4x 5x2 – 6x4 + 2x3 23x8 + 14x5 – 34x2 Your Turn!

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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

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**More Problems Polynomials 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2**

Put the following in ascending order according to the x value. 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2 12x4y2 – y5 + 3x + 8x6y3 More Problems

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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

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**Try Again! Polynomials Write in descending order: 8, 16, 2, 6, 21, 0**

2x3 + 3x5 + 4x 5x2 – 6x4 + 2x3 23x8 + 14x5 – 34x2 Try Again!

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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

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**Last Try Polynomials 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2**

Put these in descending order according to the X value 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2 12x4y2 – y5 + 3x + 8x6y3 Last Try

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**Quiz 8.4 Polynomials 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: 2x + 3x2 – 7 7xy2 – 5x3y + 2y4

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Sum 3/4 Honors Algebra Warm-up Find a if (3 a+2 ) 2 (3 3a-10 ) = 81.

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