# Polynomials with Complexesâ¦ Complex Zeros that is!

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## Objective

SWBAT identify the imaginary zeros of a polynomial function and use imaginary roots to find the standard form of a polynomial function.

#### Big Idea

Personal response systems keep students engaged and monitor their current progress as they find all zeros of a polynomial function.

## Warm-up: clicker questions

10 minutes

At the start of class, students should complete the warm-up questions on Flipchart - complex zeros and more practice (p.1-3). This question on page 2 was intended for students to apply the remainder theorem. However, I would definitely encourage students to solve the problem using any method that makes sense to them. Similarly, the question on page 3 was intended for students to apply the factor theorem.  After all students have submitted their answers, I want to take a minute or two to talk with students about the different methods they used/we could have used to solve these problems and what they would have looked like: synthetic division, long division, dividing using squares, or the most efficient methods, applying the remainder or factor theorem. The following questions would be used to help lead the discussion:

• How would we set up these problems?
• Where would we find the remainder?
• If it is a factor what would the remainder be?
• How are roots, zeros, and factors related?
• How could we use our calculator as a tool for efficiency?

Here is another great opportunity to bring our students attention to the mathematical practices… Mathematical Practice 5: Use appropriate tools strategically - Depending on how this unit plays out (and their responses to the last question), I may take some time for calculator tips here. I just want to be sure that my students understand how they could find the zeros of a polynomial function on the calculator. Specifically by using the Calculate: Zeros option on the graph menu. I will require students to still show their work of synthetic division or long division, but I think it is important they have a method to check their answers too.

10 minutes