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Understanding Polynomials: Degrees, Types, and Ordering Methods

This resource introduces students to polynomials, covering key concepts such as determining the degree of a polynomial and arranging polynomial terms in ascending or descending order. Designed by Skip Tyler from Varina High School, it explains what constitutes a polynomial and categorizes them into monomials, binomials, and trinomials. The guide clarifies important distinctions, including why certain expressions are not classified as polynomials. Practical examples and step-by-step instructions aid students in mastering polynomial identification and ordering techniques.

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Understanding Polynomials: Degrees, Types, and Ordering Methods

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  1. PolynomialsThe student will be able to: 1. find the degree of a polynomial. 2. arrange the terms of a polynomial in ascending or descending order. Designed by Skip Tyler, Varina High School

  2. What is a polynomial? A polynomial is a monomial or a sum/difference of monomials. Important Note!! An expression is not a polynomial if there is a variable in the denominator.

  3. Special Polynomials monomial - one – a #, variable or product of a # & variables binomial - two – two monomials added or subtracted trinomial - three – three monomials added or subtracted

  4. State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial

  5. The degree of a monomial is the sum of the exponents of the variables.Find the degree of each monomial. 1) 5x2 2 4a4b3c 8 -3 0

  6. To find the degree of a polynomial, find the largest degree of the terms. 1) 8x2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2 is the degree! 2) y7 + 6y4 + 3x4m4 Degrees: 7 4 8 8 is the degree!

  7. Find the degree of x5 – x3y2 + 4 • 0 • 2 • 3 • 5 • 10

  8. A polynomial is normally put in ascending or descending order. What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents. (Carnegie calls this “Standard Form” because it is what is normally used.) If there is more than one variable, you will be told which variable to put in order!

  9. Put in descending order: • 8x - 3x2 + x4 - 4 x4 - 3x2 + 8x - 4 2) Put in descending order in terms of x: 12x2y3 - 6x3y2 + 3y - 2x -6x3y2 + 12x2y3 - 2x + 3y

  10. 3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x -2x + 3y - 6x3y2 + 12x2y3 • Put in ascending order: 5a3 - 3 + 2a - a2 -3 + 2a - a2 + 5a3

  11. Write in ascending order in terms of y:x4 – x3y2 + 4xy–2x2y3 • x4 + 4xy– x3y2–2x2y3 • –2x2y3 – x3y2 + 4xy + x4 • x4 – x3y2–2x2y3 + 4xy • 4xy –2x2y3 – x3y2 + x4

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