Transcript Classifying Polynomials in Standard Form

Classifying Polynomials in
Standard Form
A necessary skill to prepare
for Algebra I
Polynomial
 “Poly”
means “many”
 “nomial” means “term” (mathematically
speaking)
 So, “polynomial” means “many terms”
 ***A polynomial is a collection of many
terms in an expression written with sums
and differences. (It uses the same variable
which may have different exponents in the
expression).
Standard Form (of a Polynomial)
 When
a polynomial is written in
standard form, it’s variables are arranged
in order from highest to lowest
exponent.
 Sometimes, this may be reversed and
written in order from lowest to highest
exponent.
Degree of a Polynomial
The
degree of a polynomial is
the degree (power) of the
term with the highest
exponent.
Terms (in a Polynomial
Expression)
 Terms
are the items being added and
subtracted.
 Each term can be one of the following
 Number alone
 Variable alone
 Number and variable joined by
multiplication
Naming a Polynomial
 Polynomials
have first and last names
like people.
 The first name comes from the
degree (highest power) of the
polynomial.
 The second name comes from the
number of terms being added and
subtracted in the expression.
First Names in Polynomials
 Constant:
When there is no variable
present (just a plain real number).
 Linear: When the highest degree of
your variables is “1”
 Quadratic: When the highest degree
of your variables is “2”
First Names continued. . .
 Cubic:
When the highest degree of
your variables is “3”.
 Quartic: When the highest degree of
your variables is “4”.
 Nth degree: A description used when
degrees higher than 4 exist as your
highest degree.
Last Names in Polynomials
 Monomial:
1 term
 Binomial: 2 terms
 Trinomial: 3 terms
 Polynomial with ____ terms:
description used when there are more
than 3 terms.
Sample Named Polynomials
Written in Standard Form
 Make a chart on your paper as
directed by the teacher and copy the
samples given. . . (teacher examples in
3-column chart: Expression,
Standard Form, Name)
Create-a-Polynomial
1.
2.
3.
4.
5.
6.
7.
Create ONE of each of the following in
Standard Form:
Cubic Binomial
Quartic polynomial with 5 terms
Linear Monomial
Quadratic Trinomial
Sixth Degree Trinomial
Constant Monomial
Eighth Degree Polynomial with 4 terms
Create-a-Polynomial continued. . .
8.
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12.
Cubic Monomial
Linear Binomial
Quadratic Binomial
Quartic Trinomial
Ninth Degree polynomial with 6 terms