111
CLASSIFYING CLASSIFYING POLYNOMIALS POLYNOMIALS by: GLORIA KENT
CLASSIFYING CLASSIFYING POLYNOMIALSPOLYNOMIALS
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 PolynomialDegree 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 PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
5xn
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
5xn “nth” degree
9 No variable Constant
8x 1st degree Linear
7x2 + 3x 2nd degree Quadratic
6x3 – 2x 3rd degree Cubic
3x4 + 5x – 1 4th degree Quartic
2x5 + 7x3 5th degree Quintic
5xn “nth” degree “nth” degree
Degree of a PolynomialDegree of a Polynomial(Each degree has a special “name”)(Each degree has a special “name”)
Let’s practice classifying polynomials by “degree”.
POLYNOMIAL1. 3z4 + 5z3 – 72. 15a + 253. 1854. 2c10 – 7c6 + 4c3 - 95. 2f3 – 7f2 + 16. 15y2
7. 9g4 – 3g + 58. 10r5 –7r9. 16n7 + 6n4 – 3n2
DEGREE NAME1. Quartic2. Linear3. Constant4. Tenth degree5. Cubic6. Quadratic7. Quartic8. Quintic9. Seventh degree
The degree name becomes the “first name” of the polynomial.
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
25x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term25x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial25x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial25x
3x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms
25x
3x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
25x
3x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
25x
3x 37 2 4x x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms
25x
3x 37 2 4x x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
25x
3x 37 2 4x x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
25x
3x 37 2 4x x
4 3 22 2 5x x x x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
Four (or more) terms
25x
3x 37 2 4x x
4 3 22 2 5x x x x
Naming PolynomialsNaming Polynomials (by number of terms)(by number of terms)
One term Monomial
Two terms Binomial
Three terms Trinomial
Four (or more) terms
Polynomial with 4 (or more) terms
25x
3x 37 2 4x x
4 3 22 2 5x x x x
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 1 term Monomial
15h
Classifying (or Naming) a Polynomial by Number of Terms
25 1 term Monomial
15h 1 term
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. 15x
2. 2e8 – 3e7 + 3e – 7
3. 6c + 5
4. 3y7 – 4y5 + 8y3
5. 64
6. 2p8 – 4p6 + 9p4 + 3p – 1
7. 25h3 – 15h2 + 18
8. 55c19 + 35
Classify by # of Terms:
1. Monomial2. Polynomial with 4 terms
3. Binomial
4. Trinomial
5. Monomial6. Polynomial with 5 terms
7. Trinomial
8. Binomial
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2
2x
2x + 7
5b2
Naming/Classifying Polynomials by
Degree (1st name) and Number of Terms (last name)
Polynomial Degree # of Terms Full Name
2 No degree (constant)
2x
2x + 7
5b2
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 (monomial)
2x
2x + 7
5b2
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 (monomial)
Constant Monomial
2x
2x + 7
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
2x + 7
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
2x + 7
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2 2nd degree (quadratic)
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2 2nd degree (quadratic)
1 term (monomial)
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 (monomial)
Constant Monomial
2x 1st degree (Linear)
1 term (monomial)
Linear Monomial
2x + 7 1st degree (linear)
2 terms (binomial)
Linear Binomial
5b2 2nd degree (quadratic)
1 term (monomial)
Quadratic Monomial
. . .more polynomials. . .5b2 + 2
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4 4th degree (quartic)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4 4th degree (quartic)
1 term (monomial)
. . .more polynomials. . .5b2 + 2 2nd degree
(quadratic)2 terms
(binomial)Quadratic Binomial
5b2 + 3b + 2 2nd degree (quadratic)
3 terms (trinomial)
Quadratic Trinomial
3f3 3rd degree (cubic)
1 term (monomial)
Cubic Monomial
2f3 – 7 3rd degree (cubic)
2 terms (binomial)
Cubic Binomial
7f3 – 2f2 + f 3rd degree (cubic)
3 terms (trinomial)
Cubic Trinomial
9k4 4th degree (quartic)
1 term (monomial)
Quartic Monomial
. . .more polynomials. . .9k4 – 3k2
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)
9k4 + 3k2 + 2
v5
v5 – 7v
f5 – 2f4 + f2
j7 - 2j5 + 7j3 - 8
. . .more polynomials. . .9k4 – 3k2 4th degree
(quartic)2 terms
(binomial)
9k4 + 3k2 + 2
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
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)
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)
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
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 (monomial)
Quintic 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 (monomial)
Quintic 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 (monomial)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
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)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
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)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
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)
Quintic Monomial
v5 – 7v 5th degree (quintic)
2 terms (binomial)
Quintic Binomial
f5 – 2f4 + f2 5th degree (quintic)
3 terms (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 (monomial)
Quintic 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 (monomial)
Quintic 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 (monomial)
Quintic 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 (monomial)
Quintic 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):
POLYNOMIAL1. 5x2 – 2x + 32. 2z + 53. 7a3 + 4a – 124. -155. 27x8 + 3x5 – 7x + 4
6. 9x4 – 37. 10x – 1858. 18x5
CLASSIFICATION / NAME
1. Quadratic Trinomial
2. Linear Binomial
3. Cubic Trinomial
4. Constant Monomial5. 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
