Prove Polynomials Can be Written Using the Dimension Theorem

[linalg]

Use the dimension theorem to show that every polynomial p(x) in Pn can be written in the form p(x)=q(x+1)-q(x) for some polynomial q(x) in Pn+1.

I need to see all the steps so that I understand how to do it.
PLease and Thank you

 

[SammyS]

Use the dimension theorem to show that every polynomial p(x) in Pn can be written in the form p(x)=q(x+1)-q(x) for some polynomial q(x) in Pn+1.

I need to see all the steps so that I understand how to do it.
PLease and Thank you

Hello linalg. Welcome to PF !

What have you tried ?

Where are you stuck?


Please look at the rules for this Forum. We won't do your work for you but will try tu help you arrive the solution.

 

[linalg]

I am actually very confused on where to start. I tried poving if it is linear independent and then kinda got lost.
Please help

 

[Ray Vickson]

Try the cases n=1 and n=2 first. That will show you what to do in general.

RGV

 

[linalg]

Thanks for your guys' help. I tried the two cases n=1 and n=2 but i am still lost. Its a homework question due tomorrow that I don't need to understand how to do it until the test in a couple weeks.

 

[Ray Vickson]

If q(x) is a polynomial of degree 2, is h(x) = q(x+1) a polynomial in x? What is its degree? What are its x-coefficients?

RGV

 

[Mark44]

I need to see all the steps so that I understand how to do it.

This isn't how it words here at Physics Forums.

 

[linalg]

Ok Mark44 just answer the question then

 

[Mark44]

Ok Mark44 just answer the question then

What question? You have not asked a single question.