# Polynomials Sprint - Let's Get Started

$\color{#D61F06} {\text{ The course is over.} }$

Let's get started. Work your way down this list of tasks. Remember to check back during the week, as tasks may get added:

Friday:

A. Read Useful Lemma to learn about it. What other questions can we apply it to?

B. It seems to me that people are not too familiar with what roots of unity are, and how to use them. This is a advanced topic, that pushes your understanding of polynomials. Try working on the following questions from the book, with a focus on using roots of unity (somewhere) in the solution. If you can't solve them after Sunday, make a post on Help Wanted.

C. Write a comment in What I Learnt. I'm sure a lot of you have learnt from this past week, but there are only 2 comments there.

$18, 28, 37, 38$

Wednesday:

A. The discussions on Polynomial Vieta and Polynomial Remainder have been opened. Join in, and share what you learnt.

B. For those who haven't seen Vieta's Formula, read the attached note. Solve the 2 questions added at the end (and struggle with the third).

C. Work on Sharky's problem Vieta might come in handy.

D. Work on Eddie's note on Having No Rational Roots.

E. Write a comment in What I Learnt.

Monday:
A. Read through pages 245 - 250 of Problem Solving Strategies. (Not the whole chapter)

B. If you have any questions about the material, ask them in Help Wanted.

C. Know the following terms:
- Polynomials, Coefficients, Degrees
- Division, Quotient, Division Algorithm
- Remainder Factor Theorem, Rational Root Theorem
- Vieta's Formula
- Roots of unity

D. Work on the following problems in the book, listed on pages 254-255. Try not to refer to solutions at the end of the chapter.
$3, 4, 5, 11, 13, 16, 17, 18.$

E. Work on the problems Polynomial Vieta and Polynomial Remainder. Solutions / Discussions will only be open in 2 days, so everyone can work on them.

F. Write a comment in What I Learnt.

G. Provide feedback, so that we can improve this experience for you.

The goal of this set is to provide exposure to problems which you likely have not encountered in school. You will learn new techniques, apply known ideas, and improve your problem solving skills. For those who are new, you can review How This Will Work to understand the expectations.

Note by Calvin Lin
6 years, 11 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

For roots of unity practice you might want to try my problem

- 6 years, 11 months ago

What's root of unity

- 6 years, 11 months ago

Refer to Help Wanted. There is an active discussion initiated by @Ananay Agarwal about root of unity.

Staff - 6 years, 11 months ago

ok

- 6 years, 11 months ago

Why has there been so little activity? Is it because it's been a while since the last update (June 27)? Or is it because everyone is celebrating July 4?

- 6 years, 11 months ago

When can we expect another update? Or is there something that I'm missing?

- 6 years, 11 months ago

That was the end. The note was published on Friday, and unlocked on Monday for discussion through the rest of the week.

I would appreciate feedback, thanks!

Staff - 6 years, 11 months ago

When is the next course starting?

- 6 years, 11 months ago

Where can I get the book ? Do I need to purchase a hard copy of book or is it a pdf available for free ?

- 5 years, 10 months ago

You can try looking for pdf copies of it online.

Staff - 5 years, 10 months ago

Sir, can you please tell me the name of the book ?

- 5 years, 10 months ago

- 6 years, 11 months ago

I've updated it with a link to the book that we're using. Thanks!

Staff - 6 years, 11 months ago

Where is the link sir ?

- 5 years, 10 months ago

Great work! (y)

- 6 years, 11 months ago

Are we expected to purchase a copy of the book? Or is there someway to view it for free?

- 6 years, 11 months ago

- 6 years, 11 months ago

thank you

- 6 years, 11 months ago

Google "arthur engel problem solving strategies" and follow the first link, which should be a pdf. By the way the above link works if you surround italicized text with "_"s.

- 6 years, 11 months ago

Hello! I actually feel that apart from referring to the book as a resource, some notes may be added to facilitate better understanding of certain topics that may be covered in the future. Eg- Functional eqaution may be covered, but for a beginner it will be very difficult to understand without proper directive. Thnx! :)

- 6 years, 11 months ago