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September 11th, 2012, 05:56 PM   #1
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Is this dividing by zero?

If you want to find the factors f(x) You dive by (x-a). You get some new function q(x) +remainder/(x-a). If (x-a) is a factor of f(x), then the remainder is zero.
Also, f(x)=(x-a)q(x)+remainder, and f(a)=(0)q(x) + remainder or just f(a)= remainder.

But Isn't it quasi dividing by zero If you divide f(x) by (x-a), while x=a? I'm thinking f/a=q+r/a, then f=a(q)+r, except when a = zero.
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September 12th, 2012, 07:18 AM   #2
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Re: Is this dividing by zero?

What you are saying is that as long as , . And, as long as , . You say "functions", but all of this only makes sense for polynomials (as you imply when you say "find the factors"). All polynomials are continuous for all x so taking the limit as x goes to a of that formula gives f(a)= q(a)(0)+ remainder= remainder.
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