Question

Is it possible to add 2 polynomials together and your answer is not a polynomial? Please provide an example and an explanation. Plz help!

Answer 1

Well, it depends on what you mean by 'polynomial'.

Do you mean something with 4 or more terms? Or do you mean just any kind of polynomial?

Answer 2

It probably means one of 4 or more terms in this case.

Answer 3

Yeah..

Answer 4

She likely wants to prove if adding two will result in anything less than 4 terms.

Answer 5

yes, x^2 + 2 add -x^2 + 2 gives 4!!

Answer 6

Well, add this:

\((2a^2 + b^3) + (9a^2 + 3b^3)\)

Answer 7

It has like terms, so we combine them..can you do that? @cobra-strikes

Answer 8

the short answer is NO polynomials are closed under addition, just as integers are closed under addition
add two integers, get an integer
add two polynomials, get a polynomial
of course it might be the zero polynomial
\[x+(x)=0\]for example, but it will be a polynomial

Answer 9

can you add two natural numbers, and get an answer that is not a natural number?

Answer 10

(for example)

Answer 11

\[x+(-x)=0\] is what i means two write ...

Answer 12

Isn't that a *cough* direct answer?

Answer 13

yea! i have 3 more sorta like this question, but its subtraction, multiplication, and division :/

Answer 14

adding,
http://www.wolframalpha.com/input/?i=y%3D0+is+a+plynomial

yes y=0 is a polynomial

Answer 15

could y'all also help me with the other 3?

Answer 16

perhaps

Answer 17

actually, my example with natural numbers is at fault because 0 is not a natural number.
I guess, to make it true, change "natural" number to a "whole" number.

Answer 18

4+(-4) \(\large\color{slate}{ \ne }\) NATURAL NUMBER

Answer 19

with whole numbers or integeres though, it would work

Answer 20

... bye:)

Answer 21

lol thank you @SolomonZelman