Grade 12 Math complex HELPP

• step-by-step process for how to find the roots of a polynomial function.
• You can use one or more questions from Assignment 1 as examples, or use your own unique examples.
• Write out a full solution of your question(s).
• Annotate your solution to point out where you use each of the following (label and draw arrows or thought bubbles):

1) Theremainder theoremand / orfactor theorem

2) Theprocess of factoring a polynomial (including how to find a first factor). Make sure you show one of the following methods: box method, synthetic division, long division.

3) Thezero product propertyfor solving a polynomial equation

4) Thesolutionsto the polynomial equation

Make connectionsto the graph of thecorresponding polynomial function (include a Desmos graph or hand sketch) in your document.

1. Start with a quartic polynomial function, in standard form. Make sure that it is factorable. Hint: Make one up by starting with the factors and expand to get your polynomial.
2. Factor your polynomial. Use the factor theorem and repeated division. Explain each step and use proper math notation and vocabulary. Use one of the methods from class (Box method, Synthetic Division, Long Division). Hint: Use Desmos at each step to verify your work
3. Include a Desmos sketch of your polynomial function, and list as many key features / characteristics as you can think of.

For this discussion, I encourage you to try usingVideo Noteto make a video posting.

For many people, the natural speaking voice is easier to process and understand than written text. Plus, it helps us to get to know each other a little better as a class :)

You do not need to show your face if you aren't comfortable with that. For example, you could show a piece of your work, and include an audio file where you talk about it. It's up to you!

To find the Video Note, go to theInsert Stufficon on the Discussion toolbar, and select Video Note

As in Activity 5, select one of the questions from Activity 8, Assignment 1 and post a full solution. As a group, make sure you post a variety of solutions, including the more complex ones involving the quadratic formula.

In your solution, include each of the following:

1) The full process of factoring the polynomial function that is part of the inequality, including using the factor theorem

2) Using the zero product property to determine zeros of the polynomial function

3) Creating an appropriate interval chart that shows intervals where the function is positive and where it is negative

4) The solution to the inequality, including a number line representation

Finally, make connections to the graph of the corresponding polynomial function (include a Desmos graph or hand sketch).

Look at the solutions of your group members. Reply to at least one other post. Use this opportunity to ask a question about a classmate's process, offer helpful feedback about a strength or include a suggestion for a next step.

Consider the important characteristics of polynomials that help you make connections between the equation and the graph in factored form:

even vs odd degree

sign of the leading coefficient (positive or negative)

end behaviours

different orders of roots (e.g. order 1 - linear, order 2 - double, order 3 - cubic)

polynomial function in factored formthat you haven't used or seen before in this course.

Identify important characteristics of your polynomial.

What do these characteristics tell you about the graph of your function?

Review other posts. Respond to two other posts:

One post where a student has described a polynomial that has characteristics in common with your function. Make direct reference to the characteristics to describe the similarities

One post where a student has described a polynomial that has characteristics that are different from those of your function. Make direct reference to the characteristics to describe the differences.

This discussion post will be assessed formally. Make sure you challenge yourself to include a variety of different characteristics and identify key connections to the graph. See the rubric

• step-by-step process for how to find the roots of a polynomial function.
• You can use one or more questions from Assignment 1 as examples, or use your own unique examples.
• Write out a full solution of your question(s).
• Annotate your solution to point out where you use each of the following (label and draw arrows or thought bubbles):

1) Theremainder theoremand / orfactor theorem

2) Theprocess of factoring a polynomial (including how to find a first factor). Make sure you show one of the following methods: box method, synthetic division, long division.

3) Thezero product propertyfor solving a polynomial equation

4) Thesolutionsto the polynomial equation

Make connectionsto the graph of thecorresponding polynomial function (include a Desmos graph or hand sketch) in your document.

• step-by-step process for how to find the roots of a polynomial function.
• You can use one or more questions from Assignment 1 as examples, or use your own unique examples.
• Write out a full solution of your question(s).
• Annotate your solution to point out where you use each of the following (label and draw arrows or thought bubbles):

1) Theremainder theoremand / orfactor theorem

2) Theprocess of factoring a polynomial (including how to find a first factor). Make sure you show one of the following methods: box method, synthetic division, long division.

3) Thezero product propertyfor solving a polynomial equation

4) Thesolutionsto the polynomial equation

Make connectionsto the graph of thecorresponding polynomial function (include a Desmos graph or hand sketch) in your document.