1 is a factor of all integers , but is -1 also a factor of all integers. I was studying rational root test in quadratic equations and it involved taking both positive and negative value of factors, so is it correct to take -1 as factor of a positive integer because say for example 2 and -2 are both factors to 4, so by this 1 and -1 should both be factors, right.
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1Look at the examples in https://en.wikipedia.org/wiki/Rational_root_theorem – Martin R Apr 04 '23 at 08:47
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Yes it does divide all integers. The integers contain both positive and negative numbers. There are two units! 1 and -1. (They are units, that is why they aren't prime.) And it is actually the case that in the integers, both 2 and -2 are prime numbers. (and 3,-3, 5,-5, you get the point). – Control Apr 04 '23 at 09:35
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Whether $-1$ is considered a factor of a number ultimately depends on context and definition.
However, in the context of the rational root test, negative numbers are factors.
Hence, in checking $p(x) = x^2 + x + 1$, you need to check $+1$ and $-1$ alike, as an example (since, after all, $1 = (-1)(-1)$).
PrincessEev
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When dealing with prime numbers and prime factors we generally only consider natural numbers (positive integers).
John
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