Is |a| a Factor of |p0| in a General Polynomial of Degree n?

[josephcollins]

Could someone please offer some assistance to answering this question?

Q) Show that if (x-a) is a factor of

(pnx^n) + (p(n-1)x^n-1) + ... p0 (General polynomial of degree n)

then |a| is a factor of |p0|.

Thanks a lot

 

[arildno]

You may write your polynomial as a product of its (possibly complex) root factors (x-r)
(Fundamental theorem of algebra)
Identify the constant term (p0) as the product of all roots r.

 

[Hurkyl]

Alternatively, see what you get when you plug in a for x.

 

[mathwonk]

just mu;ltiply out the equation you are assuming:

(x-a)(anx^(n-1) + a(n-1)x^(n-1)+...+a0) = (pnx^n) + (p(n-1)x^n-1) + ... p0 .


If you could not do this, you are not skilled yet at basic experimentation. Think about the emaning of the statement you are trying to check, then see if you can write that statement down precisely. then see if it is obvious.


(I am celebrating my birthday by having briefly all 10 of the most recent posts in this forum. I apologize if some or all of them are trivial.)

 

[arildno]

(I am celebrating my birthday by having briefly all 10 of the most recent posts in this forum. I apologize if some or all of them are trivial.)

You also deserve the title of "chief paleontologist"
(Note: I still think your excavations and answers are, in general, excellent)

 

[mathwonk]

well i had to dig pretty deep to find 10 questions i could think of answers to.