Question

Your goal for this activity is to demonstrate the proof of your polynomial identity through an algebraic proof and a numerical proof
•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 1

Hi, d-jay!
I'm sure plenty of people on OpenStudy.com would like to help you out. Can you first say what exactly? What polynomial?

Answer 2

I have to make one up

Answer 3

I don't understand how

Answer 4

Here's some I will provide:
(x – y)
(x + y)
(y + x)
(y – x)
(x + a)
(y + b)
(x2 + 2xy + y2)
(x2 – 2xy + y2)
(ax + b)
(cy + d )

These are all polynomials.

Answer 5

They have given a bunch of samples. Each one is a polynomial. They want you to combine one or more polynomials and come up with an equation.
Here I have chosen to create a polynomial by multiplying (x+a) and (x+a)
(Note: (x+a) is one of the samples listed.)
(x+a)(x+a) = x^2 + ax + ax + a^2 = x^2 + 2ax + a^2
The left hand side is (x+a)^2.
Therefore the polynomial identity is: (x+a)^2 = x^2 + 2ax + b^2
They are asking for a whole lot of other things, but this is the gist of the math part.

Answer 6

thanks I really didn't understand

Answer 7

Do you understand now??

Answer 8

What *exactly* don't you understand? Can you explain?

Answer 9

The actual polynomial would be:
(x+a)^2 = x^2 + 2ax + a^2
The right side is the polynomial. But the equation is an identity involving a polynomial.
An identity means you can put various values for the variables on the left and right and no matter what you choose the left side should match the right side.
To prove it numerically, I can choose x = 3 and a = 2 and calculate the left side and right side separately and prove they are identical (hence an identity)
(x+a)^2 = x^2 + 2ax + a^2
Let x = 3 and a = 2
LHS = (3+2)^2 = 5^2 = 25
RHS = 3^2 + (2)(2)(3) + 2^2 = 9 + 12 + 4 = 25
LHS = RHS and therefore we have proven the polynomial identity.