2 PolynomialsLesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problemsStudents will know the terms for polynomials.Students will know how to arrange polynomials in ascending and descending order.
3 PolynomialsMonomial – a number, a variable or a number and variable multiplied together. Ex: 3, x2, or 5xPolynomial – a monomial or sum of monomials. Ex: 2, x, 3x2 + 2xBinomial – the sum or difference of two monomials. Ex: 3x2 + 2xTrinomial – 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!
4 PolynomialsAscending order – increasing from the smallest to the largest. Ex: 1, 3, 4, 6, 7Descending 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.
5 PolynomialsExample 1:Arrange the terms or each polynomial so that the powers of x are in ascending order: x4 – x2 + 5x3Answer: – x2 + 5x3 + x4
7 PolynomialsExample 2:Arrange the terms or each polynomial so that the powers of x are in ascending order:8x3y – y2 + 6x2y + xy2Answer: – y2 + xy2 + 6x2y + 8x3y
8 More Problems Polynomials 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2 Put the following in ascending order according to the x value.2x2y3 + 3x3y6 + 4xy5x7y5 – 2x2y4 + 7x4y212x4y2 – y5 + 3x + 8x6y3More Problems
9 PolynomialsExample 3:Arrange the terms or each polynomial so that the powers of x are in descending order: x4 – x2 + 5x3Answer: x4 + 5x3 – x2
11 PolynomialsExample 4:Arrange the terms or each polynomial so that the powers of x are in ascending order:8x3y – y2 + 6x2y + xy2Answer: 8x3y + 6x2y + xy2 – y2
12 Last Try Polynomials 2x2y3 + 3x3y6 + 4xy 5x7y5 – 2x2y4 + 7x4y2 Put these in descending order according to the X value2x2y3 + 3x3y6 + 4xy5x7y5 – 2x2y4 + 7x4y212x4y2 – y5 + 3x + 8x6y3Last Try
13 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 + 5x2Arrange in descending order by the powers of x:2x + 3x2 – 77xy2 – 5x3y + 2y4
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