CLASSIFYING POLYNOMIALS

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