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chicagochica5
Is the difference of two polynomials always a polynomial? Explain.
no a term could cancel out
the differance is subtraction like 3x-6 - 4x+6
poly means more than one otherwise it is a monomial
what do you think @helder_edwin
yes. but monomials are only a particular case of polynomials.
so what would the answer be
if q(x) is polynomial, is -q(x) still a polynomial?
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
so yes it still is a polynomial you are correct @helder_edwin
yes its still a polynomial because....
@UnkleRhaukus can you help please?
A polynomial is a number or algebraic expression with no variables having fractional or negative exponents.
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.
@CliffSedge so for the answer i write, Yes the difference of two polynomials are always polynomials. Because why
@hartnn can you help please
the difference of two polynomials are always polynomials. Because there is no way to subtract polynomials and get something that is not a polynomial.
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.
even \(f(x)=0\) is a polynomial