Question

Is the difference of two polynomials always a polynomial? Explain.

Answer 1

Not always,

Answer 2

no a term could cancel out

Answer 3

yes it is.

Answer 4

the differance is subtraction like 3x-6 - 4x+6

Answer 5

poly means more than one otherwise it is a monomial

Answer 6

what do you think @helder_edwin

Answer 7

yes. but monomials are only a particular case of polynomials.

Answer 8

so what would the answer be

Answer 9

if q(x) is polynomial, is -q(x) still a polynomial?

Answer 10

A polynomial in one variable (i.e., a univariate polynomial) with constant coefficients is given by







(1)


The individual summands with the coefficients (usually) included are called monomials

Answer 11

so yes it still is a polynomial you are correct @helder_edwin

Answer 12

yes its still a polynomial because....

Answer 13

@UnkleRhaukus can you help please?

Answer 14

A polynomial is a number or algebraic expression with no variables having fractional or negative exponents.

Answer 15

So 5 - 2 = 3 is a difference of two polynomials yielding another polynomial.
There shouldn't be any way to subtract polynomials and get something that is not a polynomial.

Answer 16

@CliffSedge so for the answer i write, Yes the difference of two polynomials are always polynomials. Because why

Answer 17

@hartnn can you help please

Answer 18

the difference of two polynomials are always polynomials. Because there is no way to subtract polynomials and get something that is not a polynomial.

Answer 19

In more detail: Since the only way for a polynomial to become not a polynomial is if you took a root of a variable or divided by a variable, and that won't happen if all you're doing is subtracting.

Answer 20

even \(f(x)=0\) is a polynomial