1. POLYNOMIALS 9/20/2015

2. STANDARD FORM OF A POLYNOMIAL ax + bx + cx … mx + k nn-1n-2 The degree is ‘n’

3. WHAT’S THE DEGREE?

4. VIETA’S FORMULAS Degree of the polynomial

5. FIND THE FOLLOWING:

6. COMPLEX CONJUGATE THEOREM

7. WHY DOES THAT HAPPEN?

8. DESCARTES RULE OF SIGNS Helps you find out how many possible positive and negative roots a function has For POSITIVE Roots: 1. List coefficients in order 2. Count sign changes 3. Subtract 2 to account for imaginary roots For NEGATIVE Roots: 1.Solve for f(-x) and then list coefficients in order 2.Count sign changes 3.Subtract 2 to account for imaginary roots

9. LET’S DO THIS EXAMPLE TOGETHER

10. RATIONAL ROOTS THEOREM Function must have integer coefficients

11. FIND ALL RATIONAL ROOTS OF:

12. SO WHEN WE GET THE POSSIBLE ROOTS, HOW DO WE FIND OUT WHICH ONES WORK? Use synthetic division: