Add and subtract polynomial functions

Adding and subtracting polynomial functions means combining like terms—terms with the same variable and exponent—by adding or subtracting their coefficients while preserving the polynomial structure. In function notation, $(f+g)(x)=f(x)+g(x)$ and $(f-g)(x)=f(x)-g(x)$; the latter requires applying the negative sign to every term being subtracted, and cancellation may reduce the degree. This scope is limited to one-variable polynomial functions with numerical coefficients, not multivariable or abstract polynomial systems.