2. Polynomial function
A polynomial function is an expression of
finite length
For example, x2-x/4+7 is a polynomial
3. 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
4. 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.
5. 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.
6. 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.
