By the Remainder Theorem, we have p(a)=a, p(b)=b,
p(c)=c. Assuming that a,b,c are distinct, we can write
p(x)=(x-a)(x-b)(x-c)q(x)+r(x),
where r(x) is a polynomial of degree at most 2. We must have
r(a)=a, r(b)=b, r(c)=c. Hence the polynomial r(x)-x has degree
at most 2 and roots a,b,c, and must therefore be the zero
polynomial. Thus, x is the remainder.
Questions and/or comments should be directed to
Judy Downey
or Griff Elder
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Last modified: Wed Oct 18 09:12:11 CDT 2000