1. POLYNOMIALS LESSON OBJECTIVES: Determine the highest degree of a polynomial. Writing polynomials in standard form.

2. Review Let’s review some vocabulary....... Coefficient Coefficient – The number in front of the variable. Constant Constant – A number without a variable. Terms Terms – Any number, variable, or product or quotient of a number and variable. (always separated by + or – signs)

3. Polynomial These are examples of polynomials: 5X² - 2X + 3 – 3X³ + 7X - 4

4. Degree of a Polynomial The degree of a polynomial is calculated by finding the largest exponent in the polynomial.

5. Degree of a Polynomial

6. Largest exponent is 1

7. Degree of a Polynomial Largest exponent is 1 degree 1

8. Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2

9. Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2

10. Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3

11. Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3 degree 3

12. Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3 degree 3 Largest exponent is n

13. Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3 degree 3 Largest exponent is n degree n

14. Example 1 Answer the following questions about this polynomial: 1. What is the degree of the polynomial? 6

15. Example 1 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 6

16. Example 1 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 6 11

17. Example 1 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 3.What is coefficient of third degree term? 6 11 2

18. Example 2 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 3.What is coefficient of second degree term? 4 – 5 17

19. Standard Form of Polynomials When you write polynomials, you write them with the exponents in decreasing order.

20. Example 3 Write this polynomial in standard form. What term has the largest exponent?

21. Example 3 Write this polynomial in standard form. What term has the next largest exponent?

22. Example 3 Write this polynomial in standard form. What term has the next largest exponent?

23. Example 3 Write this polynomial in standard form. What term has the next largest exponent?

24. Example 3 Write this polynomial in standard form. What term has the next largest exponent?

25. Example 3 Write this polynomial in standard form. What is the last term?

26. TRY THESE: Copy them onto notebook paper first, then re-write in standard form. 1. 4x – 3x 2 2. 4x + 9 3. 6 – 3x – 7x 2 4. 9z 2 – 11z 3 + 5z – 5 5. y – 7y 5 + 15y 8 6. c 2 – 2 + 4c SOLUTIONS: 1. -3X 2 + 4X 2. 4X + 9 (stay same) 3. -7x 2 – 3x + 6 4. -11z 3 + 9z 2 + 5z – 5 5. 15y 8 – 7y 5 + y 6. c 2 + 4c - 2

27. continued... 7. -10 + 4q 4 – 8q + 3q 2 8. -2 + 7x 9. 2x 3 – x 4 + 3 10. 3x 4 – 2 – 2x 3 + 7x 11. 5 – 2x 12. 3x 6 – 4 + 2x 2 13. -2x + 5 – 4x 2 + x 3 SOLUTIONS: 7. 4q 4 + 3q 2 – 8q – 10 8. 7x – 2 9. -x 4 + 2x 3 + 3 10. 3x 4 – 2x 3 + 7x – 2 11. -2x + 5 12. 3x 6 + 2x 2 – 4 13. x 3 – 4x 2 – 2x + 5

28. INDEPENDENT PRACTICE (classwork or homework – follow teacher instructions) Copy and re-write in standard form. 1. 6x 2 + 7 – 9x 4 2. 3y – 9 – y 3 3. 9 + 7v 4. 2x + 7x 2 5. 4x 2 – 2x – x 3 – 4 6. -2x + 3 + 5x 2 7. 7z 3 – 12 + 4z 8. 3 – 3x – 4x 2 – 6x 3 9. 1 + 5x + 2x 2 10. 5y + 18y 8 – 3y 2 11. -x – 4 – 3x 2 - 6x 3 12. 9y – 9y 3 + 9y 2