# Thread: Proving a factor correct

1. ## Proving a factor correct

Hello,

I am a grade 12 functions student with an exam tomorrow morning. I was doing one last review and a question has me stumped. I would really appreciate someone's help.

This is what it is asking

"Show that (x+y) is a factor of x^8-y^8"

It seems simple, but its late here and I think I'm missing something.

Thanks again

2. Originally Posted by FunctionsStudent
Hello,

I am a grade 12 functions student with an exam tomorrow morning. I was doing one last review and a question has me stumped. I would really appreciate someone's help.

This is what it is asking

"Show that (x+y) is a factor of x^8-y^8"

It seems simple, but its late here and I think I'm missing something.

Thanks again
one way to go: keep using the difference of two squares formula:

$x^8 - y^8 = (x^4 + y^4)(x^4 - y^4) = (x^4 + y^4)(x^2 + y^2)(x^2 - y^2) = ...$

another way, use the remainder/factor theorem: if the remainder of $x^8 - y^8 \div x + y$ is 0, then $x + y$ is a factor of $x^8 - y^8$ by the factor theorem.

so use long division (or synthetic division) to show that the remainder is actually zero

3. Ah, I was trying to use synthetic division improperly, and as soon as you mentioned remainder/factor theorem I realized that was the simplest route.

x=(-y) therefore (-y)^8-y^8=0

I had one of those "Ohhh..." moments.