POLYNOMIALS 9/20/2015. STANDARD FORM OF A POLYNOMIAL ax + bx + cx … mx + k nn-1n-2 The degree is ‘n’

POLYNOMIALS9/20/2015

STANDARD FORM OF A POLYNOMIAL

ax + bx + cx … mx + kn n-1 n-2

The degree is ‘n’

WHAT’S THE DEGREE?

VIETA’S FORMULASDegree of the polynomial

FIND THE FOLLOWING:

COMPLEX CONJUGATE THEOREM

i =

3i

WHY DOES THAT HAPPEN?

• the quadratic formula

• If I solve it for a polynomial like

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 order2. Count sign changes3. Subtract 2 to account for

imaginary roots

LET’S DO THIS EXAMPLE TOGETHER

RATIONAL ROOTS THEOREM

• Function must have integer coefficients

FIND ALL RATIONAL ROOTS OF:

SO WHEN WE GET THE POSSIBLE ROOTS, HOW DO WE FIND OUT WHICH ONES WORK?

• Use synthetic division: