SOLUTION: Hi. I'm teaching myself Algebra for the GRE because I somehow missed all the math in high school and college. Anyway, my question is about relatively prime polynomials. My textbo

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Question 662822: Hi.
I'm teaching myself Algebra for the GRE because I somehow missed all the math in high school and college. Anyway, my question is about relatively prime polynomials. My textbook just says they have no common factors other than constants, and I know how to factor, but the selected answers say that these pairs aren't relatively prime:
1) 5x, x^2
2) x+x^2, 3x^3
3) 7a, a
and these pairs are:
4) t^2-4t,t^2-4
5) 2x+4, 2x^2-4
6) 64x^5+8x^3-6x, 8x^3+12x^2+24x-16
I don't see how these pairings are different. I tried breaking them down and comparing them to one another, but I'm completely stumped by how 1) isn't relatively prime but 5) is. Can you please help me figure out what I'm not seeing? Thanks!
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

The idea is, the labeling is just according to the definition.

DEFN: polynomials whose only common factors are constants considered 'relatively prime'?

1) 5x, x^2   ||  have x in common

5) 2x+4, 2x^2-4   ||Only have a 2 in common and 2 is a constant, so these are relatively prime 

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