chapter 10 - polynomials tab 1: identifying polynomials

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Chapter 10 - Polynomials Tab 1: Identifying Polynomials

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Page 1: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Chapter 10 - Polynomials

Tab 1: Identifying Polynomials

Page 2: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Definition

Polynomials : Is a monomial or a sum ofmonomialsThe prefix poly- means more than one, the suffix –nomialmean name but in math it means terms.Therefore, Polynomial means more than oneterm.Examples of Polynomials: * Terms are separated by a +

or - sign.212x³y8x² + 4x – 3x² - 9

Page 3: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Identifying Polynomials

Polynomials are identified in two ways by the number of terms and by degree.

Page 4: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Identifying Polynomials by Terms

Monomial: Mon means one, a polynomial

with one term.

Examples of Monomials:-4x

5

6x²y³

Page 5: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Identifying Polynomials by Terms

* Terms are separated by a + or - sign.

• Binomial: Bi means two, a polynomial with two terms.Examples of Binomials:

-4x + 3

x³- 225

6x²y³ - x

Page 6: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Identifying Polynomials by Terms

* Terms are separated by a + or - sign. Trinomial: Tri means three, a polynomial

with three terms.Examples of Trinomials:

8x² + 4x – 3x²y³ + xy² – y64y³ + y² – 2

* More than 3 terms is called a polynomial*

Page 7: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Identifying Polynomials by Degree

Degree of the Polynomial is determined bythe largest exponent of the variable.Examples:

5x³ + 4x² -6 has a degree of 3 Cubicx² + 4 has a degree of 2 Quadratic3x + 1 has a degree of 1 Linear2 has a degree of 0

Constant

* More than a degree of 3 , just write the number.*

Page 8: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6

3x + 1

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 9: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0

3x + 1

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 10: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant

3x + 1

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 11: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 12: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 13: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 14: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5

4x³ - 8x

5x³+4x²-6x+14

Page 15: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2

4x³ - 8x

5x³+4x²-6x+14

Page 16: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic

4x³ - 8x

5x³+4x²-6x+14

Page 17: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x

5x³+4x²-6x+14

Page 18: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x 3

5x³+4x²-6x+14

Page 19: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x 3 Cubic

5x³+4x²-6x+14

Page 20: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x 3 Cubic Binomial

5x³+4x²-6x+14

Page 21: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x 3 Cubic Binomial

5x³+4x²-6x+14 3

Page 22: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x 3 Cubic Binomial

5x³+4x²-6x+14 3 Cubic

Page 23: Chapter 10 - Polynomials Tab 1: Identifying Polynomials

Let’s Put IT All Together

Polynomial Degree Identify by Degree

Identify by Terms

6 0 Constant Monomial

3x + 1 1 Linear Binomial

-x²+2x-5 2 Quadratic Trinomial

4x³ - 8x 3 Cubic Binomial

5x³+4x²-6x+14 3 Cubic Polynomial