1. Math 71A 5.1 – Introduction to Polynomials and Polynomial Functions 1

2. A number or a number multiplied by variables is called a ________________ (also called a ________). 2 Polynomials

3. A number or a number multiplied by variables is called a ________________ (also called a ________). 3 Polynomials monomial

4. A number or a number multiplied by variables is called a ________________ (also called a ________). 4 Polynomials monomial term

5. 5 Polynomials

6. 6

7. The sum of the exponents of the variables is called the ________________ of a monomial. The numerical factor in a monomial is called the ___________________. 7 Polynomials

8. The sum of the exponents of the variables is called the ________________ of a monomial. The numerical factor in a monomial is called the ___________________. 8 Polynomials degree

9. The sum of the exponents of the variables is called the ________________ of a monomial. The numerical factor in a monomial is called the ___________________. 9 Polynomials degree coefficient

10. Ex 2. What are the degrees and coefficients of the following monomials? 10 Polynomials MonomialDegreeCoefficient 17

11. Ex 2. What are the degrees and coefficients of the following monomials? 11 Polynomials MonomialDegreeCoefficient 2 -4 17

12. Ex 2. What are the degrees and coefficients of the following monomials? 12 Polynomials MonomialDegreeCoefficient 2 -4 135 17

13. Ex 2. What are the degrees and coefficients of the following monomials? 13 Polynomials MonomialDegreeCoefficient 2 -4 135 4 2 17

14. Ex 2. What are the degrees and coefficients of the following monomials? 14 Polynomials MonomialDegreeCoefficient 2 -4 135 4 2 1 17

15. Ex 2. What are the degrees and coefficients of the following monomials? 15 Polynomials MonomialDegreeCoefficient 2 -4 135 4 2 1 2 1 17

16. Ex 2. What are the degrees and coefficients of the following monomials? 16 Polynomials MonomialDegreeCoefficient 2 -4 135 4 2 1 2 1 1 17

17. Ex 2. What are the degrees and coefficients of the following monomials? 17 Polynomials MonomialDegreeCoefficient 2 -4 135 4 2 1 2 1 1 17 0

18. 18 Polynomials

19. 19 Polynomials polynomial

20. 20 Polynomials polynomial degree

21. 21 Polynomials polynomial degree

22. A polynomial with 2 terms is called a ____________________. A polynomial with 3 terms is called a ____________________. 22 Polynomials

23. A polynomial with 2 terms is called a ____________________. A polynomial with 3 terms is called a ____________________. 23 Polynomials binomial

24. A polynomial with 2 terms is called a ____________________. A polynomial with 3 terms is called a ____________________. 24 Polynomials binomial trinomial

25. 25 Adding Polynomials

26. 26 Adding Polynomials

27. 27 Adding Polynomials

28. 28 Subtracting Polynomials

29. 29 Subtracting Polynomials

30. 30 Subtracting Polynomials

31. 31 Polynomial Functions

32. In general, polynomial functions are __________ (i.e. only have rounded curves with no sharp corners) and ________________ (i.e. don’t have breaks and can be drawn without lifting pencil). 32 Polynomial Functions

33. In general, polynomial functions are __________ (i.e. only have rounded curves with no sharp corners) and ________________ (i.e. don’t have breaks and can be drawn without lifting pencil). 33 Polynomial Functions smooth

34. In general, polynomial functions are __________ (i.e. only have rounded curves with no sharp corners) and ________________ (i.e. don’t have breaks and can be drawn without lifting pencil). 34 Polynomial Functions smooth continuous

35. Also, polynomial functions always either rise or fall as you go to the left or right (except for constant functions). 35

36. 36

37. 37 leading term

38. 38 leading term highest

39. 39 leading term highest

40. 40 leading term highest

41. 41 leading term highest

42. 42 leading term highest

43. 43 leading term highest

44. 44 leading term highest