1. Chapter 9 Polynomials

2. What are polynomials? Poly- nomial- What are monomials Mono- nomial

3. Monomials One term A monomial is a number, a variable, or the product of a number and a variable Monomials that are real numbers (no variables) are called constants

4. Examples MonomialsNot monomials 12 q 4x² 11ab 1/3r²t³ xyz a + b a b 5 – 7d 5 a² 5a 7b

5. The Degree of a monomial is the sum of the variable’s exponents ExamplesDegree

6. Exponent Rules Product of Powers Power of a Power Power of a Product Power of a Monomial Quotient of Powers Zero Exponent Negative Exponents

7. Product of Powers For any number a and all integers m and n, Examples:

8. Power of a Power For any number a, and all integers m and n Examples:

9. Power of a Product For all numbers a and b, and any integer m, Examples

10. Power of a Monomial For all numbers a and b, and any integer m, n, and p Examples:

11. Quotient of Powers For all integers m and n, and any non-zero number a, Why non-zero number a?? Examples:

12. Zero Exponent For any non-zero number a, Proof(s) Examples:

13. Negative Exponents For any nonzero number a and any integer n, Examples:

14. Scientific Notation Is a way to write really big or really small numbers A number is expressed in scientific notation when it is in the form a x 10, where 1≤ a <10 and n is an integer Examples

15. Scientific Notation?? YES??YES! 3.24 x 10 ² 89.2 x 10³ 9.0321 x 10 6.76².087 x 10 7.056 x 10 6 x 10

16. Arithmetic with numbers in scientific notation Multiplying Dividing

17. Polynomials A polynomial is a monomial or a sum of monomials. The exponents of the variables of the monomials must be positive. Examples:

18. Polynomials Monomials One term Binomials Two terms Trinomials Three terms Not polynomials

19. Degree of a polynomial Degree of each term Degree of polynomial

20. Order of Polynomial Ascending order Descending order

21. Adding and Subtracting Polynomials