1 / 18

Polynomials Warm Up Lesson

Evaluate polynomial expressions, identify coefficients, classify polynomials, and write them in standard form. Learn vocabulary related to monomials and degrees of polynomials.

paulmwalker
Download Presentation

Polynomials Warm Up Lesson

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6-3 Polynomials Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1 Holt Algebra 1

  2. Warm Up 11/09/16 Evaluate each expression for the given value of x. 1. 2x + 3; x = 22.x2+ 4; x = –3 Identify the coefficient in each term. 3. 4x34. y3 5. 2n76. –b4 7 13 4 1

  3. Essential Objectives Classify polynomials and write polynomials in standard form. Evaluate polynomial expressions.

  4. Vocabulary monomial degree of a monomial polynomial degree of a polynomial standard form of a polynomial leading coefficient quadratic cubic binomial trinomial

  5. A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents. The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.

  6. A. 4p4q3 Example: Finding the Degree of a Monomial The degree is 7. Add the exponents of the variables: 4 + 3 = 7. B. 7ed The degree is 2. Add the exponents of the variables: 1+ 1 = 2. C. 3 The degree is 0. Add the exponents of the variables: 0 = 0.

  7. a. b. c. 1.5k2m 4x 2c3 Check It Out! Find the degree of each monomial. The degree is 3. Add the exponents of the variables: 2 + 1 = 3. The degree is 1. Add the exponents of the variables: 1 = 1. The degree is 3. Add the exponents of the variables: 3 = 3.

  8. Remember! The terms of an expression are the parts being added or subtracted.

  9. A polynomialis a monomialor a sum/ difference of monomials. The degree of a polynomial is the degree of the term with the greatest degree.

  10. B. :degree 4 :degree 3 –5: degree 0 Example: Finding the Degree of a Polynomial A. 11x7 + 3x3 11x7: degree 7 3x3: degree 3 The degree of the polynomial is the greatest degree, 7. The degree of the polynomial is the greatest degree, 4.

  11. The terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in standard form. The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient.

  12. Standard form is –7x5 + 4x2 + 6x + 9. The leading coefficient is –7. Example 3A: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. 6x – 7x5 + 4x2 + 9 = –7x5 + 4x2 + 6x + 9

  13. Remember! A variable written without a coefficient has a coefficient of 1. y5 = 1y5

  14. The leading x5 + 9x3 – 4x2 + 16. The standard form is coefficient is 1. Check It Out! 16 – 4x2 + x5 + 9x3

  15. Terms Name 1 Monomial 0 Constant 2 Binomial 1 Linear 3 Trinomial Quadratic 2 Polynomial 4 or more Cubic 3 Quartic 4 Quintic 5 6 or more 6th,7th,degree and so on Some polynomials have special names based on their degree and the number of terms they have.

  16. a 6th-degree polynomial. Example 4: Classifying Polynomials acubic binomial. A. 5n3 + 4n Degree: 3 Terms: 2 B. 4y6 – 5y3 + 2y – 9 Degree: 6 Terms: 4 C. –2x a linear monomial. Degree: 1 Terms: 1

  17. Lesson Quiz: Part I Find the degree of each polynomial. 1. 7a3b2 – 2a4 + 4b –15 2. 25x2 – 3x4 Write each polynomial in standard form. Then give the leading coefficient. 3. 24g3 + 10 + 7g5 – g2 4. 14 – x4 + 3x2

  18. Lesson Quiz: Part II Classify each polynomial according to its degree and number of terms. 5. 18x2 – 12x + 5 6. 2x4 – 1

More Related