06-23-2014, 07:21 AM
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#12
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the Mathemagician~
Join Date: Nov 2005
Location: Quebec City
Age: 33
Posts: 1,320
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Re: [Math] Summation Help
Quote:
Originally Posted by SKG_Scintill
Double post, but is "b" always f(a)?
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I totally forgot about that theorem. Here's a proof:
Let f be a polynomial of degree n. The formula for dividing f(x) by (x-a) is:
f(x) = g(x)(x-a) + b, where g(x) is a polynomial of degree n-1 and b is the remainder of the division.
Let's see what is the value of f(a):
f(a) = g(a)(a-a) + b
f(a) = g(a)(0) + b
f(a) = b
QED
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