# Polynomials Sprint: What I Learnt

In this note, you will write down 1 item that you learnt, from reading the chapter, working on the problem or understanding the note. State what you liked about it, and how it could be useful. You can also add additional things that you want to find out.

For example

I learnt about the rational root theorem, which says that the rational roots of a polynomial with integer coefficients depends only on the first and last coefficient. This gives us a simple way to test for possible roots of a polynomial. I would like to know if there is a "irrational root theorem", which tells us what other roots we could try, like $\sqrt{2}$ or $1 + 2i$.

For more examples, see Adventures Of The Mind Diary.

Note by Calvin Lin
5 years, 9 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 a newcomer to Olympiad mathematics One word that describes Calvin sir......for his notes .....help......He is embodiment of wisdom who is sent to earth to help to nurture blooming minds to become torch bearers..for mathematics........

I have in my school learnt this theorem but the advance questions really was great ....I learnt how to apply this for hexamonic and heptamonic........so on polynomials

SIMPLY PUTTING SIR YOU ARE GREAT

- 5 years, 9 months ago

Wait what

- 5 years, 9 months ago

I finally learned the real reason why f(x) has a root at x = a if and only if f(x) = (x-a)(g(x))--namely, from the remainder factor theorem. This makes problems like Polynomial Remainder trivial.

- 5 years, 9 months ago