Math 50

1. Math 50 3.2 – Introduction to Polynomials; Combining Like Terms

2. An expression that is a constant or a product of a constant and variables that are raised to whole number powers is called a _________________. ex:

3. An expression that is a constant or a product of a constant and variables that are raised to whole number powers is called a _________________. ex: monomial

4. Why isn’t a monomial? Why isn’t a monomial?

5. Why isn’t a monomial? Why isn’t a monomial? Variables divided, not multiplied

6. Why isn’t a monomial? Why isn’t a monomial? Variables divided, not multiplied Has addition/subtraction

7. The numerical factor in a monomial is called the _____________________. The sum of the exponents of all variables in a monomial is called the ______________ of the monomial.

8. The numerical factor in a monomial is called the _____________________. The sum of the exponents of all variables in a monomial is called the ______________ of the monomial. coefficient

9. The numerical factor in a monomial is called the _____________________. The sum of the exponents of all variables in a monomial is called the ______________ of the monomial. coefficient degree

10. The numerical factor in a monomial is called the _____________________. The sum of the exponents of all variables in a monomial is called the ______________ of the monomial. coefficient degree Basically, count how many variables are being multiplied

11. Ex 1.

12. Ex 1.

13. Ex 1.

14. A monomial or a sum of monomials is called a ___________________. ex:

15. A monomial or a sum of monomials is called a ___________________. ex: polynomial

16. Note: In polynomials, we usually call each monomial a _______. A polynomial with exactly one term is called a _____________. (ex: ) A polynomial with exactly two terms is called a _____________. (ex: ) A polynomial with exactly three terms is called a _____________. (ex: )

17. Note: In polynomials, we usually call each monomial a _______. A polynomial with exactly one term is called a _____________. (ex: ) A polynomial with exactly two terms is called a _____________. (ex: ) A polynomial with exactly three terms is called a _____________. (ex: ) term

18. Note: In polynomials, we usually call each monomial a _______. A polynomial with exactly one term is called a _____________. (ex: ) A polynomial with exactly two terms is called a _____________. (ex: ) A polynomial with exactly three terms is called a _____________. (ex: ) term monomial

19. Note: In polynomials, we usually call each monomial a _______. A polynomial with exactly one term is called a _____________. (ex: ) A polynomial with exactly two terms is called a _____________. (ex: ) A polynomial with exactly three terms is called a _____________. (ex: ) term monomial binomial

20. Note: In polynomials, we usually call each monomial a _______. A polynomial with exactly one term is called a _____________. (ex: ) A polynomial with exactly two terms is called a _____________. (ex: ) A polynomial with exactly three terms is called a _____________. (ex: ) term monomial binomial trinomial

21. (See example at top of page again) ex:

22. (See example at top of page again) ex: trinomial

23. (See example at top of page again) ex: trinomial binomial

24. (See example at top of page again) ex: trinomial binomial trinomial

25. (See example at top of page again) ex: trinomial binomial trinomial binomial

26. (See example at top of page again) ex: trinomial binomial trinomial binomial monomial

27. (See example at top of page again) ex: trinomial binomial trinomial binomial monomial monomial

28. Ex 2.List the terms and coefficients of the polynomial .

29. Ex 2.List the terms and coefficients of the polynomial .

30. Ex 2.List the terms and coefficients of the polynomial .

31. The greatest degree of any of the terms in the polynomial is called the ___________________. Ex 3.What’s the degree of ? Ex 4.What’s the degree of ?

32. The greatest degree of any of the terms in the polynomial is called the ___________________. Ex 3.What’s the degree of ? Ex 4.What’s the degree of ? degree of the polynomial

33. The greatest degree of any of the terms in the polynomial is called the ___________________. Ex 3.What’s the degree of ? Ex 4.What’s the degree of ? degree of the polynomial

34. The greatest degree of any of the terms in the polynomial is called the ___________________. Ex 3.What’s the degree of ? Ex 4.What’s the degree of ? degree of the polynomial

35. The greatest degree of any of the terms in the polynomial is called the ___________________. Ex 3.What’s the degree of ? Ex 4.What’s the degree of ? degree of the polynomial

36. The greatest degree of any of the terms in the polynomial is called the ___________________. Ex 3.What’s the degree of ? Ex 4.What’s the degree of ? degree of the polynomial

37. Note: Polynomials are usually written in descending order of degree. Ex 5.Write in descending order of degree.

38. Note: Polynomials are usually written in descending order of degree. Ex 5.Write in descending order of degree.

39. Monomials that have the same variables raised to the same exponents are called _______________. Ex 6.Are the following pairs of monomials like terms? and and and and

40. Monomials that have the same variables raised to the same exponents are called _______________. Ex 6.Are the following pairs of monomials like terms? and and and and like terms

41. Monomials that have the same variables raised to the same exponents are called _______________. Ex 6.Are the following pairs of monomials like terms? and and and and like terms Yes

42. Monomials that have the same variables raised to the same exponents are called _______________. Ex 6.Are the following pairs of monomials like terms? and and and and like terms Yes No (first has variable , but second doesn’t)

43. Monomials that have the same variables raised to the same exponents are called _______________. Ex 6.Are the following pairs of monomials like terms? and and and and like terms Yes No (first has variable , but second doesn’t) No (first has , but second only has )

44. Monomials that have the same variables raised to the same exponents are called _______________. Ex 6.Are the following pairs of monomials like terms? and and and and like terms Yes No (first has variable , but second doesn’t) No (first has , but second only has ) No ( and are different variables—caps matters in math!)

45. Let’s simplify the algebraic expression : When combining like terms, we can just ______ their _____________________.

46. Let’s simplify the algebraic expression : When combining like terms, we can just ______ their _____________________.

47. Let’s simplify the algebraic expression : When combining like terms, we can just ______ their _____________________.

48. Let’s simplify the algebraic expression : When combining like terms, we can just ______ their _____________________.

49. Let’s simplify the algebraic expression : When combining like terms, we can just ______ their _____________________. add

50. Let’s simplify the algebraic expression : When combining like terms, we can just ______ their _____________________. add coefficients