Quick intro to the polynomials unit [monomial, binomial, trinomial, term, degree, leading coefficient, standard form, etc.], then calculating polynomial multiplicity, roots or zeros, end behavior & finally sketching graphs of polynomials with varying degree and multiplicity. Students also match polynomial equations and their corresponding graphs.

THIS PACKAGE IS A TOTAL OF 70 QUALITY PAGES!

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✫ THIS ZIP-FILE IS ALSO INCLUDED IN MY ENTIRE POLYNOMIALS UNIT BUNDLE!

✫ You might also be interested in: Introduction, End Behavior, Multiplicity, Roots / Zeros, Graphing

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Everything included with step-by-step answer keys:

- 2 Full Lessons (30 Slides)

- 6 Worksheets [front and back]! These can be split up into class and homework worksheets, as well as review worksheets and for assessments.

- DETAILED ANSWER KEYS & NOTES TO EVERYTHING!

Topics in the introductory polynomial lesson [17 Slides]:

➤ Definition: The word "polynomial" is broken down to "poly" and "nomial" ... which means many terms.

➤ Vocabulary words with examples: monomial, binomial, trinomial, term, degree, leading coefficient, root/zero, multiplicity, end behavior.

➤ Introduces multiplicity of roots and provides examples of:

- Determining a root and its corresponding multiplicity by looking at a polynomial equation in factored form.

- Sketching the graph of a polynomial function in factored form using the rules of multiplicity.

- Identifying a possible equation in factored form by looking at a polynomial graph with various multiplicity.

➤ This lesson concludes with a "Monster Review Problem". Depending on the length of class time, this problem can be used as closure of the lesson or as a Warm Up for the following class. This problem is a quintic function (degree = 5) in standard form and ultimately looks like a cubic function because 2 of its roots are imaginary. Also, one of the real roots has a multiplicity of 2. This problem reviews:

- Identifying the degree and leading coefficient.

- Converting the equation to factored form by using the following factoring skills: by grouping, difference of cubes formula, and difference of squares formula.

- Using factored-form to help in finding the x-intercepts.

- Using the quadratic formula to produce 2 complex roots.

- Sketching the graph of a function where one of the roots has a multiplicity of 2, and knowing that two of the roots will not be graphed since they are complex.

Topics in Second Lesson [13 Slides]:

➤ Students learn that the degree of a polynomial (whether it's even or odd) as well as the sign of the leading coefficient tie into determining the End Behavior [using proper notation]. Students then use this information to sketch a polynomial graph.

➤ Students sketch the graphs of polynomials with varying degree, using all the pieces of degree, roots/zeros, multiplicity and end behavior to help them.

➤ Makes very important connections that many students miss, if not pointed out, such as: "If a cubic function has 1 real root and 2 imaginary roots, how many x-intercepts will the function have? Draw a general picture."

➤ Students continue making important connections by sketching the graphs of quadratic and cubic functions with different numbers of x-intercepts. For example, sketching the graph of a quadratic function with 1 x-intercept versus none.

Worksheets Overall Topics:

- Students state the degree, classify it (linear, quadratic, etc.), and identify the leading coefficient.

- Students must match a factored-form equation to its corresponding graph. They accomplish this by identifying x-intercepts and using the rules of multiplicity to help them. What's unique about this worksheet is that it uses the same roots, but different multiplicity.

- Various polynomial graphs & equations in which students must identify the degree and whether the end behavior is the same or different.

- Given graphs, students identify any multiplicity, end behavior, and find the equation in factored form.

- Given an equation in factored form, students identify the x-intercept(s) and zero(s) of the function. They use these to sketch the graph and they also identify the end behavior using proper notation. This is repeated for each problem where the leading coefficient changes to a negative number, which affects end behavior.

-Students use their previous knowledge to identify a possible polynomial equation in factored-form by looking at the x-intercepts of a graph; then taking it one step further by using the y-intercept to find the exact equation [Note: if your curriculum does not require students to find the exact equation, you can feel free to change the directions]

Topics in This POLYNOMIALS Unit:

BUNDLE: Entire Polynomials Unit

BUNDLE: Long & Synthetic Division and Rational Roots / Zeros Theorem

1) How to Factor the Polynomial - ALL Methods Step-by-Step

2) Solve Equations by Factoring - Which Methods Do I Use?

3) Introduction, End Behavior, Multiplicity, Roots / Zeros, Graphing

4) Local/Absolute Max/Min Values & Intervals of Increase/Decrease

5) Long Division and Introducing Factor & Remainder Theorems

6) Synthetic Division and Factor & Remainder Theorems [Continued]

7) Rational Roots / Zeros Theorem and Factor & Remainder Theorems [Continued]

8) Real-World Word Problems [Degree>2 Polynomials]

9) Polynomials UNIT TESTS with Study Guide