Definition ( polynomial)
A polynomial (in one variable
) with real coefficients is a formal expression of the following form: A polynomial can be considered as a real-valued function inputting a real number
and outputting the corresponding value after plugging the value of in the formal expression.
A number
Investigate
Why does the formula
hold?
Why do we consider polynomials?
Polynomials are the easiest relation between variables: contrarily to linear functions, this relation can require powering up the variable, but no other operations are used. Quadratic polynomials (where
) occur in a lot of elementary problems, and the easiest examples to describe come from physics. For example, imagine that you are moving in a car along a highway starting at the mile marker at time with initial speed and acceleration . Then what will your position on the highway be after time has elapsed? If your acceleration is , then your position will be defined by a linear function , but the acceleration will introduce a quadratic term . This is a polynomial relation in the variable : if we rewrite in the order of the definition, .
This is a work in progress