really need help!!!?

Question

It says that two polynomials are relatively prime if they have no common factors other than constants and to tell which pairs are relatively prime:
7a, a
5x, x^2
2p^2 + 2, 2p
3a^2 - a, a^3 - 2a

I really don't get it. i tried but i really need help

Answer 1

First, take a deep breath.

Then go through them, slowly and methodically, separating the terms into what factors you can.

(1) These terms are (7 X a) and (a). (Here, "X" means "times," not the letter 'X'!) The common factor is 'a.' Now 'a' can be a "constant" in one context, but I think that in this question it's to be considered as a variable, so that these two expressions may be called "polynomials" in that variable (if of a most simple, merely linear kind).

So, they have a common factor ('a') that is "other than a constant," so by the opening statement they are NOT relatively prime. In other words, they can both be divided by 'a'.

(2) 5x and x^2; cutting to the chase, both can be divided by x, so that x is a common factor; they're NOT relatively prime.

(3) 2p^2 + 2, 2p (Thank you for writing these so clearly; a lot of people don't!):

These terms are 2 [p^2 + 1] and 2 [p]. "2" is a constant, and doesn't count according to the opening statement. (I find that definition a bit odd, never having considered the "relative primality" of polynomials before. So I may be in your position, trying to simply follow my nose and work these things out from scratch. You and I are learning this together.)

Leaving aside the "2," then, we have two polynomials that ARE relatively prime. ([p^2 + 1] and 'p' have no common factors.)

(4) These terms are a(3a -1) and a (a^2 - 2). They have a common factor 'a,' by assumption a variable in this context; therefore they are NOT relatively prime.

I hope that this helps you. Good luck!

Live long and prosper.

Answer 2

5x, x^2 is relatively prime as is2p^2+2, 2p

Answer 3

are you kidding me..?????/
it is really hard...i have no idea...