# When two polynomials are subtracted the difference is always a polynomial True or false?

## When two polynomials are subtracted the difference is always a polynomial True or false?

If you add, subtract or multiply any two polynomials then the result will be a polynomial.

### Which property of polynomials says that the product of two polynomials is also a polynomial?

When multiplying polynomials, the distributive property allows us to multiply each term of the first polynomial by each term of the second. We then add the products together and combine like terms to simplify.

#### Is a polynomial subtracted from a polynomial always a polynomial?

This is true: the result of adding two polynomials will always be another polynomial. A polynomial is an algebraic expression made up of the sum of monomials, which are products of numbers (coefficients) and variables in positive integer exponents. Thus, the number of terms in the resultant polynomial may vary.

Will the subtraction of two polynomials always result in another polynomial expression?

If we add two integers, subtract one from the other, or multiply them, the result is another integer. The same thing is true for polynomials: combining polynomials by adding, subtracting, or multiplying will always give us another polynomial.

Why is the difference of two polynomials always a polynomial?

When subtracting polynomials, the variables and their exponents do not change. Only their coefficients will possibly change. This guarantees that the difference has variables and exponents which are already classified as belonging to polynomials. Thus the difference is always a polynomial.

## What is the difference of the polynomials?

The difference between a polynomial and a polynomial function is mainly a difference of viewpoint. Given a(x) with coefficients in F: if x is regarded merely as a placeholder, then a(x) is a polynomial; if x is allowed to assume values in F, then a(x) is a polynomial function.

### Is the difference of two polynomials always a polynomial?

Yes, the difference of two polynomials is always a polynomial. Moreover, any linear combination of two (or more) polynomials is a polynomial. To prove this, recall the definition of polynomials of one variable.

#### Which property of polynomial addition says that the sum of two polynomials?

When adding polynomials, the commutative property allows us to rearrange the terms to group like terms together. Note that any two polynomials can be added or subtracted, regardless of the number of terms in each, or the degrees of the polynomials.

What is the difference of the two polynomials?

Is the difference of 2 polynomials always a polynomial?

## Is the difference of 2 polynomials a polynomial?

### Which is property of polynomial subtraction…?

The closure property says that polynomials are closed under addition, subtraction, and multiplication, which means that every time that you add, subtract, or multiply polynomials the result is always another polynomial.

#### When do you add or subtract two polynomials is the result a polynomial?

If you add, subtract or multiply any two polynomials then the result will be a polynomial. When adding or subtracting two polynomials you typically group together similar terms and add or subtract their coefficients.

Which is the closure property of a polynomial?

The answer is the closure property of polynomials. The closure property says that polynomials are closed under addition, subtraction, and multiplication, which means that every time that you add, subtract, or multiply polynomials the result is always another polynomial.

Is the multiplication of polynomials left or right?

Multiplication of polynomials is (commutative and) associative. Multiplication is left and right distributive over addition. That is, for any three polynomials, P,Q and R we have: P (Q+ R) = P Q +P R and (P +Q)R = P R + QR