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Understanding Monomials and Polynomials: Degrees and Ordering

This lesson enables students to identify the degree of polynomials, arrange polynomial terms in ascending or descending order, and understand the structure of monomials. Real-life applications, such as sports statistics and projectile motion, illustrate the relevance of polynomials. Students will learn what constitutes a polynomial and differentiate between monomials and non-polynomials. The lesson includes exercises on identifying, finding degrees, and constructing polynomials in standard form to reinforce understanding.

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Understanding Monomials and Polynomials: Degrees and Ordering

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  1. Warm-Up: Copy these notes

  2. Examples of Monomials 18 z

  3. ObjectivesThe student will be able to: 1. find the degree of a polynomial. 2. arrange the terms of a polynomial in ascending or descending order. SOL: A.2.b

  4. Why am I learning this • You can model real life situations (sports statistics, money, interest, stocks, chemistry, physics, psychology) with polynomials. • Projectile Motion- Angry Birds

  5. What does each prefix mean? mono one bi two tri three

  6. What about poly? one or more 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.

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

  8. Which polynomial is represented by X 1 X 1 X2 X • x2 + x + 1 • x2 + x + 2 • x2 + 2x + 2 • x2 + 3x + 2 • I’ve got no idea!

  9. 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

  10. 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!

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

  12. 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.

  13. 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

  14. 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

  15. 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

  16. Standard form of a polynomial Is when the polynomial is in descending order.

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