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You are watching: Is the difference of two polynomials always a polynomial


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Yes, the difference of two polynomials is constantly a polynomial. Moreover, any type of linear mix of 2 (or more) polynomials is a polynomial.

to prove this, recall the an interpretation of polynomials that one variable. They are finite sums of expressions of the type `a*x^k,` where a is a constant, x...


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Yes, the distinction of 2 polynomials is constantly a polynomial. Moreover, any type of linear combination of 2 (or more) polynomials is a polynomial.

To prove this, recall the an interpretation of polynomials that one variable. They are finite sums of expression of the kind `a*x^k,` wherein a is a constant, x is the variable and k is a non-negative integer.

For two polynomials, `P = sum_(k=0)^n a_k x^k` and also `Q= sum_(k=0)^m b_k x^k,` its linear mix is

`R= rP + sQ=sum_(k=0)^(g) (r a_k + s b_k) x^k,`

where g = max(n,m) and also zeros are provided as the preventive coefficients.

We watch that R is additionally a polynomial. The difference is obtained when r = 1 and also s = -1.

The very same is true for a linear combinations of several polynomials and also when they have actually several variables.

See more: Which Term Means Abnormal Softening Of The Nails Is Known As Hcards


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