2. Chapter 6 Lesson 2 Operations with Polynomials

3. Vocabulary  Degree of a Polynomial- The greatest degree of any term in the polynomial

4. What is a Monomial?  A monomial is the product of non- negative integer powers of variables. Consequently, a monomial has NO variable in its denominator. It has one term.  (mono implies one)  (no negative exponents, no fractional exponents)

5. Determining if a Term is Monomial  To be a monomial, a term must satisfy the following conditions:  No addition or subtraction signs  Variables cannot be in the exponent  No variables under radicals (√ )  Variables can only have positive, integer exponents.  Variables can only be multiplied together, cannot divide a variable by another variable

6. Examples MonomialsNot Monomials

7. Polynomials  In order for an equation to be considered a polynomial, it must be made up of nothing but monomials being added or subtracted together.

8. Examples Polynomial Not a Polynomial

9. Degree of a Monomial  The degree of the monomial can be found by finding the sum of all the exponents of the variables.

10. Examples

11. Degree of a Polynomial  The degree of the polynomial is equal to the highest degree of the monomials that make up the polynomial

12. Examples

13. Simplifying Polynomials  (3x 2 – 2x + 3) – (x 2 + 4x – 2)  Step 1: Distribute the -1 to remove the parentheses  3x 2 – 2x + 3 – x 2 – 4x + 2  Step 2: Group Like Terms  (3x 2 – x 2 ) + (– 2x – 4x) + (3 + 2)  Step 3: Combine Like Terms  2x 2 – 6x + 5

14. Examples

15. Simplify by Distributing  2x(7x 2 – 3x +5)  2x(7x 2 ) + 2x(– 3x) + 2x(5)  14x 3 – 6x 2 +10x

16. Examples

18. Multiplying Polynomials  (n 2 + 6n – 2)(n + 4)  n 2 (n+4) + 6n(n+4) + (-2)(n+4)  n 2 *n + n 2 *4 + 6n*n + 6n*4 + (-2)*n + (-2)*4  n 3 + 4n 2 + 6n 2 + 24n + (-2n) + (-8)  n 3 + 10n 2 + 22n – 8

19. Examples

21. Homework  Worksheet 6-2