Question

You are going to design an advertisement for a new polynomial identity that you are going to invent. Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof in an engaging way! Make it so the whole world wants to purchase your polynomial identity and can't imagine living without it!

Answer 1

You may do this by making a flier, a newspaper or magazine advertisement, making an infomercial video or audio recording, or designing a visual presentation for investors through a flowchart or PowerPoint.

You must:

Label and display your new polynomial identity
Prove that it is true through an algebraic proof, identifying each step
Demonstrate that your polynomial identity works on numerical relationships

Answer 2

@SolomonZelman

Answer 3

@uri

Answer 4

have you come up with a new polynomial identity..?

Answer 5

Yes

Answer 6

It says:

1. Label and display your new polynomial identity
2. Prove that it is true through an algebraic proof, identifying each step
3. Demonstrate that your polynomial identity works on numerical relationships

Answer 7

How about (6-2) Would that work?

Answer 8

well its the difference of 2 degree 1 polynomials...

Answer 9

Ok so what would you do?

Answer 10

how would you prove it algebraically

Answer 11

Wait so does mine work? We can use (6-2) ?

Answer 12

yes but you need to prove it....

Answer 13

Ok so what would I say?

Answer 14

well you could say P(x) = a and then H(x) = b

then the difference between the polynomials P(x) - H(x) = a - b

start with that... how do you prove subtraction works...

Answer 15

@campbell_st Ok so is that it?

Answer 16

@SolomonZelman

Answer 17

well I'm not sure...

Answer 18

oh...ok. I will ask someone else. Thanks for helping

Answer 19

Do you know how to do this one?

Answer 20

Well, I would try to pick something a little harder. (Rather than subtracting two constant polynomials.)

Answer 21

Ok what would you do?

Answer 22

I am not even sure what the instructions exactly are for this assignment, but I would (perhaps) try to show how to find x-intercepts for any quadratic polynomial \(\large\color{black}{ \displaystyle y=\color{red}{\rm a} x^2+\color{green}{\rm b}x+\color{blue}{\rm c} }\).

Answer 23

1. Label and display your new polynomial identity
2. Prove that it is true through an algebraic proof, identifying each step
3. Demonstrate that your polynomial identity works on numerical relationships

Answer 24

I mean I would like you to come up with the idea for the assignment though.
(something from the section which this is coming from)

Answer 25

(x-y) was an example of what I could use.

Answer 26

(x-y)=constant (though)

Answer 27

like
x-y=4

Answer 28

that is a polynomial, but what would your identity then be ?

Answer 29

Are you allowed to prove rules that people have already come up with ?

Answer 30

(that **mathematicians** have already come up with )