Polynomial function

Desirae O.

Cecilia M.

Polynomial function

A polynomial function is an expression of finite length

For example, x2-x/4+7 is a polynomial

Polynomial functions

A polynomial is either zero, or can be written as the sum of one or more non-zero terms

Forming a sum of several terms produces a polynomial. For example, the following is a polynomial

Real world The concentration, in parts per million, of a certain drug in the bloodstream after t hours is

given by the polynomial

-0.05t^2 + 2t + 2

Find the concentration after 2 hr.

To find the concentration after 2 hr, we evaluate the polynomial for

t = 2:

-0.05t^2 + 2t + 2 = -0.05(2)^2 + 2(2) + 2

--------------------------= -0.05(4) + 4 + 2

---------------------------= -0.2 + 4 + 2

---------------------------= 5.8

The concentration after 2 hr is 5.8 parts per million.

Polynomial function

Zero of Multiplicity k If  is a factor of a polynomial function f and 

is not a factor of f, then r is called a zero of  multiplicity k of f.

Nature

Where are polynomial functions found in nature?

If you look at a cross section of a honeycomb, you see a pattern of hexagons. This pattern is one hexagon, surrounded by 6 more hexagons, surrounded by 12 hexagons, etc. The total number of hexagons can be modeled by f(x) = 3r2 – 3r + 1, where r is the number of rings and f(r) is the number of hexagons.

Graphs

Examples

EX: 3x5 + 2x4 – 5x3 + x2 + 1

n = 5, a0 = 3, a1 = 2, a2 = -5, a3 = 1, a4 = 0 and a5 = 1

Example

5x3 − 4x2 + 7x − 8.

Example

EX: 3x5 + 2x4 – 5x3 + x2 + 1

n = 5, a0 = 3, a1 = 2, a2 = -5, a3 = 1, a4 = 0 and a5 = 1

Example

Nature

Real World

Nature

Real World