Definition 1. A polynomial is a finite sum of terms in which all
variables have whole number
exponents (recall whole numbers are positive and include 0) and no variable
appears in the denom-
EX 1. -
1. The following are not polynomials. State why not:
2. Here are a couple examples of polynomials:
Recall that the degree of a term is the sum of the
exponents of the variables. The leading
term of a polynomial is the term of highest degree and the leading
coefficient is the coefficient of
the leading term.
EX 2. For the polynomial -7x6 + 5x4 - 2x2 + 1 we have:
Degree of the polynomial
We can classify polynomials in a couple of ways. First by the number of terms:
EX 3. For example we would write x + 6x2 + 2x3 - 1 as
2x3 + 6x2 + x - 1
Where we start with the highest degree term and continue in descending order.
5.1.1 Polynomial Functions
Polynomials can also be written as function (using function notation).
EX 4. The following are polynomial functions.
• f(x) = x2 + 3x + 2
• P(x) = 2x3 - 3x2 + x - 7
When written as a function, we can graph polynomials.
EX 5. -
1. Graph y = x2
The graph we get is called a parabola. All quadratic
polynomials have parabolas as graphs.
In this case the parabola opens upwards. Whenever the leading coefficient is
parabola opens upwards.
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