Thread: Proof

the polynomial where a, b,c,d are all integers. If p and q are two relatively prime integers, show that if is a factor P(x), then p is a factor d, and q is a factor of a.

please, i need some explanation, thank you.

Originally Posted by Heinsbergrelatz

the polynomial where a, b,c,d are all integers. If p and q are two relatively prime integers, show that if is a factor P(x), then p is a factor d, and q is a factor of a.

please, i need some explanation, thank you.

What explanation do you seek ?

The assertion is quite obvious.

If is a factor of , and is a third-degree polynomial, it means that there exists a second-degree polynomial such that .

Let us write S(x) as the polynomial it's supposed to be:



Now you do the rest.

can somebody complete the proof please? im not trying to get it the easy way, i just want a proper proof from someone more experienced...


thanks

Heinsberg, I gave you about 3/4 of a complete proof. You just have to show that you are putting some effort of your own into it.

Do what you can, even if it is erroneous, and I'll be happy to point out any mistakes, or suggest the next step if you get stuck. It will cost me more time and brainpower than it would to just finish what I began in my previous post, but it will give me the rare luxury of not feeling that I'm being fooled into doing somebody's work for them.

Although it might seem completely absurd, here it goes..

When q is a factor of a, there must be some " " to equal a.same goes for when p is a factor of d.

now of we expand the second degree polynomial with the factor it goes;



thereby; and

can you correct any mistake you see?? thanks

Originally Posted by Heinsbergrelatz

Although it might seem completely absurd, here it goes..

When q is a factor of a, there must be some " " to equal a.same goes for when p is a factor of d.

now of we expand the second degree polynomial with the factor it goes;



thereby; and

can you correct any mistake you see?? thanks

That's beautiful.

That's beautiful.

sarcasm?? or you really mean it?? im not being suspicious but i have seen many sarcastic compliments in this forum.. But if its not a sarcasm, thanks

Originally Posted by Heinsbergrelatz

That's beautiful.

sarcasm?? or you really mean it?? im not being suspicious but i have seen many sarcastic compliments in this forum.. But if its not a sarcasm, thanks

Your proof is correct, and it really is that simple.

Originally Posted by Heinsbergrelatz

That's beautiful.

sarcasm?? or you really mean it?? im not being suspicious but i have seen many sarcastic compliments in this forum.. But if its not a sarcasm, thanks

No sarcasm. sincere statement, which was reinforced by Dr. Rocket

Heinsberg, you seem reluctant to believe this, but it's a fact: you've done it, man!

I'm genuinely glad. Keep up the good work.

Thanks Everyone for the confirmation :-D

I'm genuinely glad. Keep up the good work.

thanks