Factor theorem

Watch this thread
chatterclaw73
Badges: 9
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 3 years ago
#1
Show that (x-p) is a factor of (x-q)^7+(q-p)^7.

I have put x=p to get f(p)=(p-q)^7. Then (p-q)(p-q)^6. I do not know how to continue.

I have also tried putting x=q to get (q-p)(q-p)^6. Thanks in advance for any pointers.
0
reply
chatterclaw73
Badges: 9
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report Thread starter 3 years ago
#2
Show that x-p is a factor of (x-q)^7+(q-p)^7.

I have put x=p to get f(p)=(p-q)^7=(p-q)(p-q)^6 but then I do not know how to continue.

I have also tried x=q to get (q--p)^7=(q-p)(q-p)^6. Thanks in advance for any pointers.
0
reply
RDKGames
Badges: 20
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report 3 years ago
#3
(Original post by chatterclaw73)
Show that x-p is a factor of (x-q)^7+(q-p)^7.

I have put x=p to get f(p)=(p-q)^7=(p-q)(p-q)^6 but then I do not know how to continue.

I have also tried x=q to get (q--p)^7=(q-p)(q-p)^6. Thanks in advance for any pointers.
x-p is a factor if, and only if, x=p is a solution to (x-q)^7 + (q-p)^7 = 0.

So, if you put in x=p into the function, you get:

(p-q)^7 + (q-p)^7

Can you show that this is indeed zero?
0
reply
chatterclaw73
Badges: 9
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report Thread starter 3 years ago
#4
Thanks!
(Original post by RDKGames)
x-p is a factor if, and only if, x=p is a solution to (x-q)^7 + (q-p)^7 = 0.

So, if you put in x=p into the function, you get:

(p-q)^7 + (q-p)^7

Can you show that this is indeed zero?
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest

How are you feeling about your SQA results?

They're better than I expected (20)
31.75%
They're what I expected (19)
30.16%
They're worse than what I expected (24)
38.1%

Watched Threads

View All