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!

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:

Answer 1

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
WARNING! No identities used in the lesson may be submitted. Create your own. See what happens when different binomials or trinomials are combined. Below is a list of some sample factors you may use to help develop your own identity.
(x – y)
(x + y)
(y + x)
(y – x)
(x + a)
(y + b)
(x2 + 2xy + y2)
(x2 – 2xy + y2)
(ax + b)
(cy + d)
My Work :
(ax + b)(cx + d) We will use this to create a polynomial identity
acx^2 + adx + bcx +bd
acx^2 + (ad+bc)x + bd
(ax+b)(cx+d) = acx^2 + (ad+bc)x + bd

Answer 2

Now all I need to do is prove the numerical expression

Answer 3

Help Me @iGreen @amistre64 @satellite73

Answer 4

youve already proved it ....

Answer 5

I have ?

Answer 6

youve worked from your factors into its identity .. that constitutes a direct proof.

Answer 7

if we had stated that (ax+b)(cx+d) = ac x^2 + (ad + bc)x + bd

then we would have to show why such a statement was true

Answer 8

@amistre64 It says 'numerical proof'..all I see is variables.. :l

Answer 9

I mean: She said she had to proof the 'numerical expression'.

Answer 10

it mentions nothing of a numerical proof

'Demonstrate that your polynomial identity works on numerical relationships'

Answer 11

a demonstration is not a proof

Answer 12

Actully it says 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!

Answer 13

pfft, to many words in the middle to actually reads lol

Answer 14

No worrys

Answer 15

insted of abcd, pick your favorite numbers to play with

Answer 16

Yeah, just input numbers in there. Then distribute..it should be easy.

Answer 17

and for the record, as i already stated ... there are no 'numerical' proofs. only demonstrations that satisfy proof for those specific values

Answer 18

Ok how about 2 and 6

Answer 19

2 numbers are not 4 numbers, technically speaking

Answer 20

-1 0 1 2

Answer 21

Ok now ?

Answer 22

now use them .....

Answer 23

He gave you the 4 numbers, now plug them in here: (ax + b)(cx + d)

Answer 24

Oh how

Answer 25

How would i plug it in @iGreen

Answer 26

A = -1
B = 0
C = 1
D = 2

Answer 27

So then ( -1x + 0 ) ( 1x + 2 ) Now ?

Answer 28

It would just be (-x + 0)(x + 2)

-x + 0 = ?

Answer 29

Would it be 0

Answer 30

No any number + 0 is the same thing it was before.

2 + 0 = 2
123 + 0 = 123
651 + 0 = 651

Answer 31

So -x + 0 = ?

Answer 32

-x sorry

Answer 33

Yep. So now we have (-x)(x + 2)

Now distribute.

What's -x * x?

And -x * 2?

Answer 34

X

Answer 35

-x * x = ?

Answer 36

x

Answer 37

No..you will represent it as an exponent.

\(-x \cdot x = -x^2\)

Answer 38

Okay, so what's -2 * x?

Answer 39

2 * -x*

Answer 40

2x

Answer 41

Not quite, it's -2x.

Remember, a negative times a positive is always a negative.

So our final result is \(-x^2 - 2x\).

Answer 42

THANK U SO MUCH FOR HELPING ME @iGreen

Answer 43

No problem.