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# Question Help watch

1. I got asked to research this question for homework but I have absolutely no clue:

Prove that if (x-p) is a factor of f(x) then f(p) = 0

Thanks in advance for any help
2. (Original post by OldSkoolCanary)
I got asked to research this question for homework but I have absolutely no clue:

Prove that if (x-p) is a factor of f(x) then f(p) = 0

Thanks in advance for any help
Is f(x) a polynomial? It doesn't matter too much, but that's usually the context of these kinds of questions.

Anyway, (x - p) is a factor so you can write: f(x) = (x - p)q(x), for some other function q. What can you say about f(p) now?
3. (Original post by aMathsDude)
Is f(x) a polynomial? It doesn't matter too much, but that's usually the context of these kinds of questions.

Anyway, (x - p) is a factor so you can write: f(x) = (x - p)q(x), for some other function q. What can you say about f(p) now?
I’m not sure, f(p)=f(x)/q(x)? Sorry we’ve only just started this content so I’m not very confident on it
4. (Original post by OldSkoolCanary)
I’m not sure, f(p)=f(x)/q(x)? Sorry we’ve only just started this content so I’m not very confident on it
Not quite: We have f(x) = (x - p)q(x). So just plug in p to both sides. What is (x - p) when x = p?

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