Thread: What is a coefficient in a polynomial?
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Old August 20th, 2009, 01:23 PM
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Originally Posted by blaskode View Post
I was working out of I. M. Gelfand's Algebra and encountered the following problem:

"Imagine that the polynomial (1+x-y)^3 is converted to the standard form. What is the sum of all the coefficients?"

Now, if "-1" is considered as a coefficient, this is an easy problem: (1+1-1)^3 = 1, but if "-1" is not considered a coefficient, I don't know how to do the problem without expanding the polynomial to standard form. Expanding this polynomial to standard form isn't difficult, but what if the polynomial were (1+2x)^200 instead?
In this example I would say 1 is not a coefficient but I am by no means sure
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