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## Polynomials

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**Polynomials**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**• Write in ascending order: 8, 16, 2, 6, 21, 0 • Write in ascending order: • 2x3 + 3x5 + 4x • 5x2 – 6x4 + 2x3 • 23x8 + 14x5 – 34x2 Your Turn!**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. • 2x2y3 + 3x3y6 + 4xy • 5x7y5 – 2x2y4 + 7x4y2 • 12x4y2 – y5 + 3x + 8x6y3 More Problems**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**• Write in descending order: 8, 16, 2, 6, 21, 0 • Write in descending order: • 2x3 + 3x5 + 4x • 5x2 – 6x4 + 2x3 • 23x8 + 14x5 – 34x2 Try Again!**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 • 2x2y3 + 3x3y6 + 4xy • 5x7y5 – 2x2y4 + 7x4y2 • 12x4y2 – y5 + 3x + 8x6y3 Last Try**Polynomials**Quiz 8.4 • 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: • 2x + 3x2 – 7 • 7xy2 – 5x3y + 2y4