Polynomial Functions

• Fundamental Theorem of Algebra: a polynomial with degree n, will have exactly n roots (some may be real, some may be imaginary)

𝑃𝑜𝑙𝑦𝑛𝑜𝑚𝑎𝑖𝑙𝑠 h𝑤𝑖𝑡 𝑟𝑒𝑎𝑙𝑟𝑜𝑜𝑡𝑠

Polynomials with some real and some imaginary roots

Use a calculator to find all roots of 1. y=x3 -4x2 -2x + 8

2. 12x3 – 19x2 –x + 6

3) Write a polynomial function with roots 2, 4, and -3

4) Write a polynomial -1,2, and -7

Remember imaginary numbers?• Imaginary number (i) = √-1

i0-i=i2=i3=I4=

5) Write a polynomial with roots 3, 2i, -2i

a) Write a polynomial function that best models the data

b) Predict the amount of waster produced in 2015