CLASSIFYING
POLYNOMIALS
by:
GLORIA KENT
Today’s Objectives:



Classify a polynomial by it’s degree.
Classify a polynomial by it’s number of
terms
“Name” a polynomial by it’s “first and
last names” determined by it’s degree
and number of terms.
Degree of a Polynomial
The degree of a polynomial is
calculated by finding the largest
exponent in the polynomial.
(Learned in previous lesson on
Writing Polynomials in Standard
Form)
Degree of a Polynomial
(Each degree has a special “name”)
9
Degree of a Polynomial
(Each degree has a special “name”)
9
No variable
Degree of a Polynomial
(Each degree has a special “name”)
9
No variable
Constant
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
No variable
Constant
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
No variable
1st degree
Constant
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
No variable
Constant
1st degree
Linear
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
No variable
Constant
1st degree
Linear
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
No variable
Constant
1st degree
Linear
2nd degree
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Quartic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
2x5 + 7x3
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Quartic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
2x5 + 7x3
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Quartic
5th degree
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
2x5 + 7x3
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Quartic
5th degree
Quintic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
2x5 + 7x3
5xn
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Quartic
5th degree
Quintic
Degree of a Polynomial
(Each degree has a special “name”)
9
8x
7x2 + 3x
6x3 – 2x
3x4 + 5x – 1
2x5 + 7x3
5xn
No variable
Constant
1st degree
Linear
2nd degree
Quadratic
3rd degree
Cubic
4th degree
Quartic
5th degree
Quintic
“nth” degree
Degree of a Polynomial
(Each degree has a special “name”)
No variable
Constant
9
st degree
1
Linear
8x
nd degree
2
Quadratic
2
7x + 3x
rd degree
3
Cubic
3
6x – 2x
th degree
4
Quartic
4
3x + 5x – 1
th degree
5
Quintic
5
3
2x + 7x
“nth” degree
“nth” degree
5xn
Let’s practice classifying polynomials
by “degree”.
1.
2.
3.
4.
5.
6.
7.
8.
9.
POLYNOMIAL
3z4 + 5z3 – 7
15a + 25
185
2c10 – 7c6 + 4c3 - 9
2f3 – 7f2 + 1
15y2
9g4 – 3g + 5
10r5 –7r
16n7 + 6n4 – 3n2
1.
2.
3.
4.
5.
6.
7.
8.
9.
DEGREE NAME
Quartic
Linear
Constant
Tenth degree
Cubic
Quadratic
Quartic
Quintic
Seventh degree
The degree name becomes the “first name” of the polynomial.
Naming Polynomials
(by number of terms)
5x
2
Naming Polynomials
(by number of terms)
5x
2
One term
Naming Polynomials
(by number of terms)
5x
2
One term
Monomial
Naming Polynomials
(by number of terms)
5x
2
x3
One term
Monomial
Naming Polynomials
(by number of terms)
5x
2
x3
One term
Two terms
Monomial
Naming Polynomials
(by number of terms)
5x
2
x3
One term
Monomial
Two terms
Binomial
Naming Polynomials
(by number of terms)
5x
2
x3
7 x3  2 x  4
One term
Monomial
Two terms
Binomial
Naming Polynomials
(by number of terms)
5x
2
One term
Monomial
x3
Two terms
Binomial
7 x3  2 x  4
Three terms
Naming Polynomials
(by number of terms)
5x
2
One term
Monomial
x3
Two terms
Binomial
7 x3  2 x  4
Three terms
Trinomial
Naming Polynomials
(by number of terms)
2
One term
Monomial
x3
Two terms
Binomial
7 x3  2 x  4
Three terms
Trinomial
5x
x 4  2 x3  2 x 2  5 x
Naming Polynomials
(by number of terms)
5x
2
One term
Monomial
x3
Two terms
Binomial
7 x3  2 x  4
Three terms
Trinomial
x 4  2 x3  2 x 2  5 x
Four (or more)
terms
Naming Polynomials
(by number of terms)
5x
2
One term
Monomial
x3
Two terms
Binomial
7 x3  2 x  4
Three terms
Trinomial
x  2 x  2 x  5x
4
3
2
Four (or more) Polynomial with 4
(or more) terms
terms
Classifying (or Naming) a
Polynomial by Number of Terms
25
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
Classifying (or Naming) a
Polynomial by Number of Terms
25
15h
1 term
Monomial
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
15h
1 term
Monomial
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
4b10 + 2b8 – 7b6 - 8
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
4b10 + 2b8 – 7b6 - 8
4 (or more)
terms
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
4b10 + 2b8 – 7b6 - 8
4 (or more)
terms
Polynomial
with 4 terms
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
4b10 + 2b8 – 7b6 - 8
4 (or more)
terms
Polynomial
with 4 terms
8j7 – 3j5 + 2j4 - j2 - 6j + 7
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
4b10 + 2b8 – 7b6 - 8
4 (or more)
terms
Polynomial
with 4 terms
8j7 – 3j5 + 2j4 - j2 - 6j + 7
6 terms
Classifying (or Naming) a
Polynomial by Number of Terms
25
1 term
Monomial
15h
1 term
Monomial
25h3 + 7
2 terms
Binomial
3t7 – 4t6 + 12
3 terms
Trinomial
4b10 + 2b8 – 7b6 - 8
4 (or more)
terms
Polynomial
with 4 terms
8j7 – 3j5 + 2j4 - j2 - 6j + 7
6 terms
Polynomial
with 6 terms
The term name becomes the “last name” of a polynomial.
Let’s practice classifying a
polynomial by “number of terms”.
Polynomial
1.
2.
3.
4.
5.
6.
7.
8.
Classify by # of Terms:
1. Monomial
15x
2.
2e8 – 3e7 + 3e – 7
3.
6c + 5
4.
3y7 – 4y5 + 8y3
5.
64
2p8 – 4p6 + 9p4 + 3p – 1 6.
7.
25h3 – 15h2 + 18
8.
55c19 + 35
Polynomial with 4 terms
Binomial
Trinomial
Monomial
Polynomial with 5 terms
Trinomial
Binomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
2
2x
2x + 7
5b2
Degree
# of Terms
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
2x
2x + 7
5b2
# of Terms
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
# of Terms
2
No degree
(constant)
1 term
(monomial)
2x
2x + 7
5b2
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
2x
2x + 7
5b2
# of Terms
Full Name
1 term
Constant
(monomial) Monomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
2x
1st degree
(Linear)
2x + 7
5b2
# of Terms
Full Name
1 term
Constant
(monomial) Monomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
(monomial)
2x + 7
5b2
# of Terms
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
5b2
# of Terms
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
1st degree
(linear)
5b2
# of Terms
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
1st degree
(linear)
5b2
# of Terms
2 terms
(binomial)
Full Name
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
1st degree
(linear)
5b2
# of Terms
2 terms
(binomial)
Full Name
Linear
Binomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
# of Terms
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
1st degree
(linear)
5b2
2nd degree
(quadratic)
2 terms
(binomial)
Full Name
Linear
Binomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
# of Terms
Full Name
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
1st degree
(linear)
2 terms
(binomial)
5b2
2nd degree
(quadratic)
1 term
(monomial)
Linear
Binomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms
(last name)
Polynomial
Degree
# of Terms
2
No degree
(constant)
1 term
Constant
(monomial) Monomial
2x
1st degree
(Linear)
1 term
Linear
(monomial) Monomial
2x + 7
1st degree
(linear)
5b2
2nd degree
(quadratic)
2 terms
(binomial)
Full Name
Linear
Binomial
1 term
Quadratic
(monomial) Monomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
2 terms
(binomial)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
2 terms Quadratic
(binomial) Binomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
2nd degree
(quadratic)
2 terms Quadratic
(binomial) Binomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
2nd degree
(quadratic)
2 terms Quadratic
(binomial) Binomial
3 terms
(trinomial)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
2nd degree
(quadratic)
2 terms
(binomial)
3 terms
(trinomial)
Quadratic
Binomial
Quadratic
Trinomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
(quadratic)
2nd degree
(quadratic)
3rd degree
(cubic)
2 terms
(binomial)
3 terms
(trinomial)
Quadratic
Binomial
Quadratic
Trinomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms
(quadratic) (binomial)
2nd degree
3 terms
(quadratic) (trinomial)
3rd degree
1 term
(cubic)
(monomial)
Quadratic
Binomial
Quadratic
Trinomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms
(quadratic) (binomial)
2nd degree
3 terms
(quadratic) (trinomial)
3rd degree
1 term
(cubic)
(monomial)
Quadratic
Binomial
Quadratic
Trinomial
Cubic
Monomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms
(quadratic) (binomial)
2nd degree
3 terms
(quadratic) (trinomial)
3rd degree
1 term
(cubic)
(monomial)
3rd degree
(cubic)
Quadratic
Binomial
Quadratic
Trinomial
Cubic
Monomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms
(quadratic) (binomial)
2nd degree
3 terms
(quadratic) (trinomial)
3rd degree
1 term
(cubic)
(monomial)
3rd degree
2 terms
(cubic)
(binomial)
Quadratic
Binomial
Quadratic
Trinomial
Cubic
Monomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
3rd degree
(cubic)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
3rd degree
3 terms
(cubic)
(trinomial)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
3rd degree
3 terms Cubic
(cubic)
(trinomial) Trinomial
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
3rd degree
3 terms Cubic
(cubic)
(trinomial) Trinomial
4th degree
(quartic)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
3rd degree
3 terms Cubic
(cubic)
(trinomial) Trinomial
4th degree
1 term
(quartic)
(monomial)
. . .more polynomials. . .
5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
2nd degree
2 terms Quadratic
(quadratic) (binomial) Binomial
2nd degree
3 terms Quadratic
(quadratic) (trinomial) Trinomial
3rd degree
1 term
Cubic
(cubic)
(monomial) Monomial
3rd degree
2 terms Cubic
(cubic)
(binomial) Binomial
3rd degree
3 terms Cubic
(cubic)
(trinomial) Trinomial
4th degree
1 term
Quartic
(quartic)
(monomial) Monomial
. . .more polynomials. . .
9k4 – 3k2
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
4th degree
(quartic)
. . .more polynomials. . .
9k4 – 3k2
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
4th degree
(quartic)
2 terms
(binomial)
. . .more polynomials. . .
9k4 – 3k2
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
9k4 + 3k2 + 2
4th degree
(quartic)
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
2 terms
(binomial)
Quartic
Binomial
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
Quartic
Binomial
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
(monomial)
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
2 terms
(binomial)
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
2 terms
(binomial)
Quintic
Binomial
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
f5 – 2f4 + f2
5th degree
(quintic)
j7 - 2j5 + 7j3 - 8
2 terms
(binomial)
Quintic
Binomial
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
2 terms
(binomial)
f5 – 2f4 + f2
5th degree
(quintic)
3 terms
(trinomial)
j7 - 2j5 + 7j3 - 8
Quintic
Binomial
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
2 terms
(binomial)
Quintic
Binomial
f5 – 2f4 + f2
5th degree
(quintic)
3 terms
(trinomial)
Quintic
Trinomial
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
2 terms
(binomial)
Quintic
Binomial
f5 – 2f4 + f2
5th degree
(quintic)
3 terms
(trinomial)
Quintic
Trinomial
j7 - 2j5 + 7j3 - 8
7th degree
(7th degree)
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
2 terms
(binomial)
Quintic
Binomial
f5 – 2f4 + f2
5th degree
(quintic)
3 terms
(trinomial)
Quintic
Trinomial
j7 - 2j5 + 7j3 - 8
7th degree
(7th degree)
4 terms
(polynomial
with 4 terms)
. . .more polynomials. . .
9k4 – 3k2
4th degree
(quartic)
2 terms
(binomial)
Quartic
Binomial
9k4 + 3k2 + 2
4th degree
(quartic)
3 terms
(trinomial)
Quartic
Trinomial
v5
5th degree
(quintic)
1 term
Quintic
(monomial) Monomial
v5 – 7v
5th degree
(quintic)
2 terms
(binomial)
Quintic
Binomial
f5 – 2f4 + f2
5th degree
(quintic)
3 terms
(trinomial)
Quintic
Trinomial
j7 - 2j5 + 7j3 - 8
7th degree
(7th degree)
4 terms
(polynomial
with 4 terms)
7th degree
polynomial
with 4 terms
Can you name them now? Give it a
try. . . copy and classify (2 columns):
1.
2.
3.
4.
5.
POLYNOMIAL
5x2 – 2x + 3
2z + 5
7a3 + 4a – 12
-15
27x8 + 3x5 – 7x + 4
6. 9x4 – 3
7. 10x – 185
8. 18x5
CLASSIFICATION / NAME
1. Quadratic Trinomial
2. Linear Binomial
3. Cubic Trinomial
4. Constant Monomial
5. 8th Degree Polynomial with
4 terms.
6. Quartic Binomial
7. Linear Binomial
8. Quintic Monomial
. . .more practice. . .
9. 19z25
10. 6n7 + 3n5 – 4n
11. 189
12. 15g5 + 3g4 – 3g – 7
13. 3x9 + 12
14. 6z3 – 2z2 + 4z + 7
15. 9c
16. 15b2 – b + 51
9. 25th degree Monomial
10. 7th degree Trinomial
11. Constant Monomial
12. Quintic polynomial
with 4 terms
13. 9th degree Binomial
14. Cubic polynomial
with 4 terms.
15. Linear Monomial
16. Quadratic Trinomial
Create-A-Polynomial Activity:
• You will need one sheet of paper, a pencil, and your
notes on Classifying Polynomials.
• You will be given the names of some polynomials.
YOU must create a correct matching example, but
REMEMBER:
– Answers must be in standard form.
– Each problem can only use one variable throughout the
problem (see examples in notes from powerpoint).
– All variable powers in each example must have DIFFERENT
exponents (again, see examples in notes from powerpoint).
– There can only be one constant in each problem.
• You will need two columns on your paper.
– Left column title: Polynomial Name
– Right column title: Polynomial in Standard Form.
Create - A – Polynomial Activity:
Copy each polynomial name. Create your own polynomial
to match ( 2 columns). Partner/Independent work (pairs).
1. 6th degree polynomial
with 4 terms.
2. Linear Monomial
3. Quadratic Trinomial
4. Constant Monomial
5. Cubic Binomial
6. Quartic Monomial
7. Quintic polynomial with
5 terms.
8. Linear Binomial
9. Cubic Trinomial
10. Quadratic Binomial
11. Quintic Trinomial
12. Constant Monomial
13. Cubic Monomial
14. 10th degree polynomial
with 6 terms
15. 8th degree Binomial
16. 20th degree Trinomial