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Introduction to Polynomials

Learning Targets. I will be able to:. Identifying Parts Of A Monomial. Classify polynomials by the number of terms. Classify Polynomials By Degree. Introduction to Polynomials. Identifying Parts Of A Monomial. Exponent. Exponent. Coefficient. Coefficient. Variable. Variable.

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Introduction to Polynomials

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  1. Learning Targets I will be able to: Identifying Parts Of A Monomial Classify polynomials by the number of terms Classify Polynomials By Degree Introduction to Polynomials

  2. Identifying Parts Of A Monomial Exponent Exponent Coefficient Coefficient Variable Variable Let’s try an example: Identify the coefficient, variable, and exponent:

  3. Ways to Classify Polynomials We can classify polynomials by the number of terms: Monomial: 1 term Think about other words with the prefix mono: monotone, monochromatic, monologue Binomial: 2 terms Think about other words with the prefix bi: bicycle, bifocals, bimonthly Trinomial: 3 terms Think about other words with the prefix tri: tricycle, triathlon, triceratops Polynomial: 4 or more terms Think about other words with the prefix poly: polytheistic, polygon Polynomials are fun! Let’s take a closer look at classifying polynomials by number of terms...

  4. Classifying Polynomials By Number Of Terms Monomial:a number, a variable, or the product of a number and one or more variables. We are also going to call this a term. Let’s check out some examples of monomials: A monomial with no variables is called a constant.

  5. Classifying Polynomials By Number Of Terms Binomial:a polynomial with 2 terms Let’s check out some examples of binomials: Trinomial:a polynomial with 3 terms Let’s check out some examples of trinomials:

  6. Classifying Polynomials By Degree Example 1: Finding the degree of a Monomial: The sum of the exponents of its variables. Finding the degree of a Polynomial: The same as that of its term with the greatest degree. Example 2: Example 1: Example 2:

  7. 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.

  8. A. 4p4q3 Example 1: Finding the Degree of a Monomial Find the degree of each monomial. The degree is 7. Add the exponents of the variables: 4 + 3 = 7. B. 7ed C. 3

  9. a. b. b. 1.5k2m 4x 2c3 Check It Out! Example 1 Find the degree of each monomial.

  10. Classifying Polynomials By Degree Finding the degree of a Polynomial: The same as that of its term with the greatest degree. Example 2: Example 1:

  11. 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.

  12. B. Example 2: Finding the Degree of a Polynomial And its name Find the degree of each polynomial. A. 11x7 + 3x3 11x7: degree 7 3x3: degree 3 Find the degree of each term. The degree of the polynomial is the greatest degree, 7, so it’s 7th. The degree of the polynomial is the greatest degree, 4, so it’s quartic.

  13. Check It Out! Example 2 Find the degree and the name of each polynomial. a. 5x – 6 b. x3y2 + x2y3 – x4 + 2

  14. Classifying Polynomials By Degree

  15. Square Roots Variables as the exponent Negatives as the exponent Non-Examples of Polynomials Remember... these are NOT polynomials! Fractions, Division

  16. 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.

  17. 6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9 2 Degree 1 5 2 5 1 0 0 –7x5 + 4x2 + 6x + 9. The leading The standard form is 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 Find the degree of each term. Then arrange them in descending order:

  18. Example 3B: Writing Polynomials in Standard Form Write the polynomial in standard form. Then give the leading coefficient. y2 + y6 − 3y

  19. Check It Out! Example 3a Write the polynomial in standard form. Give the leading coefficient. Then name it by degree and number of terms. 16 – 4x2 + x5 + 9x3

  20. Check It Out! Example 3b Write the polynomial in standard form. Give the leading coefficient. Then name it by degree and number of terms. 18y5 – 3y8 + 14y

  21. Example 4: Classifying Polynomials Classify each polynomial according to its degree and number of terms. A. 5n3 + 4n 5n3 + 4n is acubic binomial. Degree 3 Terms 2 B. 4y6 – 5y3 + 2y – 9 C. –2x

  22. Classify each polynomial according to its degree and number of terms. D. x3 + x2 – x + 2 E. 6 F. –3y8 + 18y5+ 14y

  23. Lesson Closing 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 5 4 7g5 + 24g3 – g2 + 10; 7 –x4 + 3x2 + 14; –1

  24. Lesson Closing: Part II Classify each polynomial according to its degree and number of terms. quadratic trinomial 5. 18x2 – 12x + 5 6. 2x4 – 1 quartic binomial

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