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Polynomials and Polynomial Functions

Polynomials and Polynomial Functions. Algebra 2: Unit 4. Chapter 6 Lesson 1: Using Properties of Exponents. California State Standards. Lesson Goals. Students are adept at operations involving polynomials. Use properties of exponents to evaluate and simplify expressions involving powers.

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Polynomials and Polynomial Functions

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  1. Polynomials and Polynomial Functions Algebra 2: Unit 4

  2. Chapter 6 Lesson 1:Using Properties of Exponents California State Standards Lesson Goals • Students are adept at operations involving polynomials. • Use properties of exponents to evaluate and simplify expressions involving powers. ESLRs: Becoming Competent Learners and Complex Thinkers

  3. Properties of Exponents Product of Powers: when multiplying factors with the same base add the exponents. Examples:

  4. Properties of Exponents Power of Product : when a product is raised to a power each factor can be raised to that power Examples:

  5. Properties of Exponents Quotient of Powers : when dividing factors with the same base subtract the exponents. Examples:

  6. Properties of Exponents Power of a Quotient : when a quotient is raised to a power each factor can be raised to that power Examples:

  7. Properties of Exponents Power of Power : when raising a power to a power multiply the exponents. Examples:

  8. Properties of Exponents Negative Exponents : when a negative exponent means “use the reciprocal” Examples:

  9. Properties of Exponents Zero Exponent : anything raised to the zero power equals 1 Examples:

  10. You Try Simplify the expression.

  11. You Try Simplify the expression.

  12. You Try Simplify the expression.

  13. You Try Simplify the expression.

  14. You Try Simplify the expression.

  15. Example Find an expression for the area of the triangle.

  16. Today’s Assignment • p. 326: 1 – 14

  17. Check Assignment • p. 326: 1 – 14, 62, 66, 83

  18. Product of Powers

  19. Power of Powers Product of Powers Zero Exponent

  20. Power of Powers

  21. Power of Quotients Product of Powers Zero Exponent

  22. Negative Exponent Power of Quotients

  23. Quotient of Powers Negative Exponents

  24. Quotient of Powers Zero Exponent

  25. Power of Product Product of Powers Negative Exponents

  26. Negative Exponents Product of Powers

  27. Power of Quotients Negative Exponents

  28. Quotient of Powers Negative Exponents

  29. Power of Product Quotient of Powers

  30. Unit 4 6 Lesson 1b:More Exponent Practice and Review Chapter 5 California State Standards Lesson Goals • Students are adept at operations involving polynomials. • Use properties of exponents to evaluate and simplify expressions involving powers. • Use properties of exponents with scientific notation ESLRs: Becoming Competent Learners and Complex Thinkers

  31. Example Find an expression for the area of the circle.

  32. Scientific Notation Very large and very small numbers can be written in a way to help make the number easier to work with. indicates the number of places the decimal point moved a number between 1 and 10

  33. Example Rewrite in scientific notation.

  34. Example Rewrite in scientific notation.

  35. Example Rewrite in standard form.

  36. Example Rewrite in standard form.

  37. Example Simplify the expression. You have to actually divide 1.41 by 1.09

  38. Example Simplify the expression. You have to actually multiply 1.04 and 1.39

  39. Example The red blood cells, white blood cells, and platelets found in human blood are all generated from the same stem cells. In laboratory experiments, scientists have found that as few as 10 stem cells can grow into 1,200,000,000,000 platelets in just four weeks. The number of white blood cells generated was 0.025 times the number of platelets. How many white blood cells were generated?

  40. You Try Simplify the expression.

  41. You Try In 1996, the population of the United States was approximately 265,280,000 people. The area of the United States is approximately 3,780,000 square miles. Use scientific notation to find the population per square mile in the United States.

  42. You Try Mercury travels approximately 226,000,000 miles around the sun. It takes Mercury approximately 2100 hours to revolve around sun. Find the speed of Mercury as it revolves around the sun.

  43. You Try There is approximately 580 computers per 1000 people in the U.S. If the population of the U.S. is 316,923,282, how many computers are there?

  44. Today’s Assignment • p. 321: 16 – 56 m

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