Question

Are polynomial expressions closed under multiplication? Explain.

Answer 1

I remember seeing this question before, and I think the answer is yes under certain conditions. I'd recommend getting a second opinion, but what it means to be closed is that if you multiply polynomials together, the result is still a polynomial.

Answer 2

e.g. x^2+2 and x-x^3+5 are both polynomials in x. If you multiply them together, you get:
x^3-x^5+5x^2+2x-2x^3+10 which is also a polynomial.

Answer 3

if you multiply a polinomial with another do you get a polynomial?

Answer 4

I think I remember someone saying that it isn't always the case, but I forget the reasoning used.

Answer 5

The set P(x) of polynomials with real coefficients is a vector space over R

Answer 6

what? i do not understand

Answer 7

Don't worry about this part, @chicagochica5

@zzr0ck3r , what if the coefficients aren't real?

Answer 8

then I dont think its closed, but I have never seen any proof regarding this so I dont know.

Answer 9

Yeah, I'm in that same boat...

@chicagochica5 - let's just assume that where you're at, you're only going to see polynomials with real coefficients, so I think you're safe to say that yes, they are closed under multiplication.

Answer 10

but what about the explaining part, what do i say

Answer 11

If you multiply two polinomials together than you obtain another polinomial, thus it is closed under multiplication.

do you need to prove it?

Answer 12

no @zzr0ck3r
I do not need to prove it

Answer 13

Thanks alot for the help @CliffSedge and @zzr0ck3r

Answer 14

polynomial*