## chicagochica5 3 years ago Is the difference of two polynomials always a polynomial? Explain.

1. gjhfdfg

Not always,

2. Decart

no a term could cancel out

3. helder_edwin

yes it is.

4. Decart

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

5. Decart

poly means more than one otherwise it is a monomial

6. Decart

what do you think @helder_edwin

7. helder_edwin

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

8. chicagochica5

so what would the answer be

9. helder_edwin

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

10. Decart

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

11. Decart

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

12. chicagochica5

yes its still a polynomial because....

13. chicagochica5

14. CliffSedge

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

15. CliffSedge

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.

16. chicagochica5

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

17. chicagochica5

18. 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.

19. CliffSedge

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.

20. UnkleRhaukus

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