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1. Polynomials

3. Vocabulary Monomial: A number, a variable or the product of a number and one or more variables. Polynomial: A monomial or a sum of monomials. Binomial: A polynomial with exactly two terms. Trinomial: A polynomial with exactly three terms. Coefficient: A numerical factor in a term of an algebraic expression.

4. Vocabulary Degree of a monomial: The sum of the exponents of all of the variables in the monomial. Degree of a polynomial in one variable: The largest exponent of that variable. Standard form: When the terms of a polynomial are arranged from the largest exponent to the smallest exponent in decreasing order.

7. Classify the polynomials by degree and number of terms. Examples Polynomial a. b. c. d. Degree Number of Terms Classify by number of terms Zero 1 Monomial First 2 Binomial Second 2 Binomial Third 3 Trinomial

9. Examples Write the polynomials in standard form. Remember: The lead coefficient should be positive in standard form. To do this, multiply the polynomial by –1 using the distributive property.

10. Practice Write the polynomials in standard form and identify the polynomial by degree and number of terms. 1. 2.

11. Problem 1 This is a trinomial. The trinomial’s degree is 3.

12. Problem 2 This is a 2 nd degree, or quadratic, trinomial.

14. Add Like Terms + 2x 2 + 3x + 2 x 2 + x + 1 = 3x 2 + 4x +3 Or you could add the trinomials in a column

15. Just like adding like-terms + 2x 2 + 3x + 2 x 2 + x + 1 3x 2 + 4x +3 Start with the trinomials in a column + 2x 2 + 3x + 2 Combine the trinomials going down

17. (3x 2 +5x) + (4 -6x -2x 2 ) 3x 2 +5x -2x 2 -6x + 4 + 0 x 2 -x + 4 It might be helpful to use a zero as a placeholder.

18. Find the difference - (3x 2 - 2x + 3) x 2 + 2x - 4 -2x 2 + 4x - 7 Start with the trinomials in a column - (3x 2 - 2x + 3) The negative sign outside of the parentheses is really a negative 1 that is multiplied by all the terms inside. - 3x 2 + 2x - 3)

19. Try One. - (10x 2 + 3x + 2) 12x 2 +5x + 11 2x 2 + 2x + 9 Reminder: Start with the trinomials in a column - (10x 2 + 3x + 2) The negative sign outside of the parentheses is really a negative 1 that is multiplied by all the terms inside. - 10x 2 - 3x - 2

20. Special Thanks to Public Television Station KLVX for the basic outline of the first 12 slides of this presentation