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Math 50

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

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Math 50

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  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

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