anonymous
  • anonymous
Is the difference of two polynomials always a polynomial? Explain.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Not always,
anonymous
  • anonymous
no a term could cancel out
helder_edwin
  • helder_edwin
yes it is.

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anonymous
  • anonymous
the differance is subtraction like 3x-6 - 4x+6
anonymous
  • anonymous
poly means more than one otherwise it is a monomial
anonymous
  • anonymous
what do you think @helder_edwin
helder_edwin
  • helder_edwin
yes. but monomials are only a particular case of polynomials.
anonymous
  • anonymous
so what would the answer be
helder_edwin
  • helder_edwin
if q(x) is polynomial, is -q(x) still a polynomial?
anonymous
  • anonymous
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
anonymous
  • anonymous
so yes it still is a polynomial you are correct @helder_edwin
anonymous
  • anonymous
yes its still a polynomial because....
anonymous
  • anonymous
@UnkleRhaukus can you help please?
anonymous
  • anonymous
A polynomial is a number or algebraic expression with no variables having fractional or negative exponents.
anonymous
  • anonymous
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.
anonymous
  • anonymous
@CliffSedge so for the answer i write, Yes the difference of two polynomials are always polynomials. Because why
anonymous
  • anonymous
@hartnn can you help please
hartnn
  • hartnn
the difference of two polynomials are always polynomials. Because there is no way to subtract polynomials and get something that is not a polynomial.
anonymous
  • anonymous
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.
UnkleRhaukus
  • UnkleRhaukus
even \(f(x)=0\) is a polynomial

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