Factor theorem Watch

chatterclaw73
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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.
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chatterclaw73
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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.
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RDKGames
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(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?
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chatterclaw73
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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?
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