5.3 Polynomials and Polynomial Functions
The following “words” are discussed in your text quite nicely. Hopefully, you have already read this
section and are somewhat familiar with them. I will not define them as part of this lecture, but will use
them. You will need to be able to identify and/or explain each.
Term
Trinomial
Leading term
Quartic
Polynomial
Term of a polynomial
Leading coefficient
Monomial
Degree of a term
Degree of a polynomial
Binomial
Coefficient of a term
Like terms
2 x  4 x 2  5  10 x 3 is a polynomial. Generally speaking, this expression would be
written such that the terms are in descending order in accordance with their degree. This
would result in:
10 x 3  4 x 2  2 x  5
a.
b.
c.
d.
e.
This polynomial has 4 terms.
The leading term is 10x3
The leading coefficient is 10.
The coefficient of the second term is 4, third term is -2, and fourth term is -5.
The degree of the first term is 3, second term is 2, third term is 1, and fourth term
is 0.
f. There are no like terms.
g. The degree of the polynomial is 3.
h. This polynomial has no special name. It is not a monomial, binomial, nor trinomial.
Written in the format P( x)  10 x  4 x  2 x  5 , we would refer to the equation as a
3
2
“polynomial function.” If we were looking for P ( 3) , we would simply be expected to
substitute the value -3 in for x and then simplify.
P(3)  10 x3  4 x 2  2 x  5
 10(3)  4(3)  2( 3)  5
 10(-27)  4(9)  6  5
 270  36  6  5
 233
3
2
Great
example of
a top down
approach.
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You will be expected to use functions to obtain estimates (or actual values) as well as
read a graph.
a) What will we do to answer the first question?
b) What is the answer to the second question?
I’ve already told you that this is a graph of a function. How could you tell, just by looking
at the graph, that it is indeed a function?
What is the domain of the function? ________________
What is the range of the function? ________________
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Homework:
94
Give the answer only in interval notation.
126 Copy the formula, substitute in the values, solve top down.
128 Follow the directions in the text. When you make the table, if you draw lines, use a
ruler. Use graph paper for the graph of the polynomial.
MML/Quiz due ____________ TextHW due ____________
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