Polynomials Polynomials Types of Polynomials About Polynomials Graphing
![Polynomials Polynomials](https://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-1.jpg)
Polynomials
![Polynomials • • Types of Polynomials About Polynomials Graphing Polynomials Evaluating Polynomials Polynomials • • Types of Polynomials About Polynomials Graphing Polynomials Evaluating Polynomials](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-2.jpg)
Polynomials • • Types of Polynomials About Polynomials Graphing Polynomials Evaluating Polynomials
![Types of Polynomials • • Monomial Binomial Trinomial Polynomial Types of Polynomials • • Monomial Binomial Trinomial Polynomial](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-3.jpg)
Types of Polynomials • • Monomial Binomial Trinomial Polynomial
![Types of Polynomials A polynomial is a broad term for a function that only Types of Polynomials A polynomial is a broad term for a function that only](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-4.jpg)
Types of Polynomials A polynomial is a broad term for a function that only has many terms with positive integer exponents. is not a polynomial.
![About Polynomials • Standard form of a polynomial is when the terms of a About Polynomials • Standard form of a polynomial is when the terms of a](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-5.jpg)
About Polynomials • Standard form of a polynomial is when the terms of a polynomial are written in descending order of exponents. is not in standard form. is in standard form.
![Rewrite the Polynomials in Standard Form Rewrite the Polynomials in Standard Form](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-6.jpg)
Rewrite the Polynomials in Standard Form
![About Polynomials • The leading coefficient is number of the term with the highest About Polynomials • The leading coefficient is number of the term with the highest](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-7.jpg)
About Polynomials • The leading coefficient is number of the term with the highest degree.
![Identify the Leading Coefficient Identify the Leading Coefficient](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-8.jpg)
Identify the Leading Coefficient
![About Polynomials • The degree of the polynomial is the greatest exponent. About Polynomials • The degree of the polynomial is the greatest exponent.](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-9.jpg)
About Polynomials • The degree of the polynomial is the greatest exponent.
![Identify the Degree of the Polynomial Identify the Degree of the Polynomial](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-10.jpg)
Identify the Degree of the Polynomial
![Graphs of Polynomials y 10 8 6 4 2 x -10 -8 -6 -4 Graphs of Polynomials y 10 8 6 4 2 x -10 -8 -6 -4](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-11.jpg)
Graphs of Polynomials y 10 8 6 4 2 x -10 -8 -6 -4 -2 -2 -4 -6 -8 -10 2 4 6 8 10
![Even Exponents • Positive Leading Coefficient 10 -8 -6 -4 • Negative Leading Coefficient Even Exponents • Positive Leading Coefficient 10 -8 -6 -4 • Negative Leading Coefficient](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-12.jpg)
Even Exponents • Positive Leading Coefficient 10 -8 -6 -4 • Negative Leading Coefficient y 10 8 8 6 6 4 4 2 2 -2 2 4 6 8 10 x -10 -8 -6 -4 -2 y 2 -2 -2 -4 -4 -6 -6 -8 -8 -10 4 6 8 10 x
![Odd Exponents • Positive Leading Coefficient 10 -8 -6 -4 • Negative Leading Coefficient Odd Exponents • Positive Leading Coefficient 10 -8 -6 -4 • Negative Leading Coefficient](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-13.jpg)
Odd Exponents • Positive Leading Coefficient 10 -8 -6 -4 • Negative Leading Coefficient y 10 8 8 6 6 4 4 2 2 -2 2 4 6 8 10 x -10 -8 -6 -4 -2 y 2 -2 -2 -4 -4 -6 -6 -8 -8 -10 4 6 8 10 x
![Graph on your Calculator Graph on your Calculator](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-14.jpg)
Graph on your Calculator
![Evaluating Polynomials Using Synthetic Substitution Evaluating Polynomials Using Synthetic Substitution](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-15.jpg)
Evaluating Polynomials Using Synthetic Substitution
![Why not just “plug it in? ” • Don’t really need a calculator. • Why not just “plug it in? ” • Don’t really need a calculator. •](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-16.jpg)
Why not just “plug it in? ” • Don’t really need a calculator. • We’ll use the idea to make dividing polynomials, which can be difficult, an easier task.
![1. Rewrite the coefficients and put the “ 2” we’re evaluating to the side. 1. Rewrite the coefficients and put the “ 2” we’re evaluating to the side.](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-17.jpg)
1. Rewrite the coefficients and put the “ 2” we’re evaluating to the side. 2 -3 -4 8 2|
![2. Bring down the “ 2”. 2 -3 2| 2 -4 8 2. Bring down the “ 2”. 2 -3 2| 2 -4 8](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-18.jpg)
2. Bring down the “ 2”. 2 -3 2| 2 -4 8
![3. Multiply the “ 2” on the side by the “ 2” that was 3. Multiply the “ 2” on the side by the “ 2” that was](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-19.jpg)
3. Multiply the “ 2” on the side by the “ 2” that was brought down and put product below “-3”. 2 -3 4 2| x 2 = -4 8
![4. Add -3 and 4 and write sum below. 2 2| 2 -3 +4 4. Add -3 and 4 and write sum below. 2 2| 2 -3 +4](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-20.jpg)
4. Add -3 and 4 and write sum below. 2 2| 2 -3 +4 1 -4 8
![5. Multiply the “ 2” on the side by the “ 1” that was 5. Multiply the “ 2” on the side by the “ 1” that was](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-21.jpg)
5. Multiply the “ 2” on the side by the “ 1” that was brought down and put product below “-4”. 2 2| 2 x -3 +4 1 -4 2 = 8
![6. Add -4 and 2 and write sum below. 2 2| 2 -3 4 6. Add -4 and 2 and write sum below. 2 2| 2 -3 4](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-22.jpg)
6. Add -4 and 2 and write sum below. 2 2| 2 -3 4 1 -4 +2 -2 8
![7. Multiply the “ 2” on the side by the “-2” that was brought 7. Multiply the “ 2” on the side by the “-2” that was brought](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-23.jpg)
7. Multiply the “ 2” on the side by the “-2” that was brought down and put product below “ 8”. 2 2| 2 x -3 4 1 -4 +2 -2 8 -4 =
![8. Add 8 and -4 and write sum below. 2 -3 -4 8 2| 8. Add 8 and -4 and write sum below. 2 -3 -4 8 2|](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-24.jpg)
8. Add 8 and -4 and write sum below. 2 -3 -4 8 2| 4 +2 -4 2 1 -2 4
![You try one! You try one!](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-25.jpg)
You try one!
![Try a Tricky One! Try a Tricky One!](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-26.jpg)
Try a Tricky One!
![](http://slidetodoc.com/presentation_image_h/05835df52208801949e93c34e6023f01/image-27.jpg)
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