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Exploring Polynomials: Terms, Degrees, & Coefficients

Learn to write polynomials in standard form, identify leading coefficients, classify by terms and degrees, and find roots. Practice finding degrees of monomials and understanding polynomial roots.

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Exploring Polynomials: Terms, Degrees, & Coefficients

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  1. Polynomials 10.0 Given a set of polynomials, students will write standard form and find leading coefficient

  2. Main Idea & Vocabulary (don’t write) • 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 polynomial is a monomial or a sum or difference of monomials.

  3. Write this down • monomial • polynomial • One term • x, y², 4vw, 3x⁴y² More than one term x + y² 4vw - 3x⁴y² 3x⁴y² - y² + 4vw

  4. More Vocabulary (don’t write) • The degree of a polynomial is the degree of the term with the greatest degree. • The standard form of a polynomial is written with the terms in order from greatest degree to least degree. • The leading coefficient is the coefficient of the first term of a polynomial written in standard form.

  5. Write this down • ex. 4x² + 3 + 2x⁴ - 5x³ + x 2x⁴ - 5x³ + 4x² + x + 3 Degree: 4 Leading Coefficient: 2

  6. Ex 2 – Standard Form

  7. Practice 2

  8. Classifying Polynomials • Some polynomials have special names based on their degree and the number of terms they have.

  9. Ex 3 - Classifying Polynomials

  10. Practice 3

  11. Ex 5 Identifying Roots of Polynomials

  12. Practice 5

  13. Review • What is a monomial? • What is a polynomial? • How do you find the degree of a polynomial? • What does the root of a polynomial represent?

  14. Practice 1

  15. Ex 1 Finding the degree of a monomial

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