1. f(x)=x 2 + 2x Degree? How many zeros What are the zeros?

2. f(x)=x 2 + 2x Degree? How many zeros What are the zeros? 2 2 nd x = -2, x = 0

3. h(x)= x 3 - x Degree? How many zeros? What are the zeros?

4. h(x)= x 3 - x Degree? How many zeros? What are the zeros? 3 rd 3 x = -1, 0, 1

5. j(x) = -x 3 +2x 2 +3x Degree? How many zeros? What are the zeros?

6. j(x) = -x 3 +2x 2 +3x Degree? How many zeros? What are the zeros? 3 rd 3 x = -1, 0, 3

7. k(x)= x 4 -5x 2 + 4 Degree? How many zeros? What are the zeros?

8. k(x)= x 4 -5x 2 + 4 Degree? How many zeros? What are the zeros? 4 th 4 x = -2, -1, 1, 2

9. l(x) = -(x 4 -5x 2 + 4) Degree? How many zeros? What are the zeros?

10. l(x) = -(x 4 -5x 2 + 4) Degree? How many zeros? What are the zeros? 4 th 4 x = -2, -1, 1, 2

11. m(x)=1/2(x 5 +x 4 -7x 3 -22x 2 + 24x) Degree? How many zeros? What are the zeros?

12. m(x)=1/2(x 5 +x 4 -7x 3 -22x 2 + 24x) Degree? How many zeros? What are the zeros? 5 th 5 x = -3, -2, 0, 1, 2

13. n(x)=-1/2(x 5 +x 4 -7x 3 -22x 2 + 24x) What are the zeroes? How many zeroes? Degree?

14. n(x)=-1/2(x 5 +x 4 -7x 3 -22x 2 + 24x) What are the zeros? How many zeros? Degree? 5 th 5 x = -4, -3, 0, 1, 2

15. Zeros and degree What is the relationship between degree and number of zeros?

16. Zeros and degree What is the relationship between degree and number of zeros? They are the same.

17. Zeroes and degree What is the relationship between degree and number of zeros? Graph the following polynomial: ◦y=(x-1)(x-3)  x-intercepts?  Zeroes?  Number of zeroes?  Degree? y

18. (x-1)(x-3)=x 2 –x-3x+3 = x 2 -4x+3 Factored form To find the zeros, set each factor =0 Standard form (x-1)=0 X=1 (x-3)=0 X=3

19. Write the standard form of the equation for the polynomial function with the given zeros Steps: Example: Use the zeroes to write the factors: (x - the zero) Write as a function in factored form. Multiply (Foil) and simplify 0, 4 and -2 (x-0)(x-4)(x+2) f(x) = x(x-4)(x+2) f(x) = x(x 2 +2x-4x-8) f(x)= x(x 2 - 2x - 8) f(x) = x 3 - 2x 2 – 8x

20. Write the standard form of the equation for the polynomial function with the given zeros 1, 3(multiplicity 2) f(x) = (x-1)(x-3)(x-3) f(x) = (x 2 -3x – x +3)(x-3) f(x) = (x 2 - 4x + 3)(x–3) f(x) = x 3 - 3x 2 - 4x 2 + 12x +3x– 9 f(x) = x 3 - 7x 2 +15x-9 Multiplicity means that a zero is used as a factor more than once

21. For each function, determine the zeros and their multiplicity 1. y=(x-3)(x+2) 2 2. y=x(x-5) 10 (x+4) 2

22. For each function, determine the zeros and their multiplicity 1. y=(x-3)(x+2) 2 2. y=x(x-5) 10 (x+4) 2 x = 3 (mult. 1) x = -2 (mult. 2) x = 0 (mult. 1) x = 5 (mult. 10) x = -4 (mult. 2)