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# Which operation between two polynomials will not always result in a polynomial?

Updated: 4/28/2022

Wiki User

8y ago

Division of one polynomial by another one.

Wiki User

8y ago

Wiki User

8y ago

Division and exponentiation are two basic operations.

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Q: Which operation between two polynomials will not always result in a polynomial?
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### Can the sum of three polynomials again be a polynomial?

The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also a polynomial.

No. Even if the answer is zero, zero is still a polynomial.

yes

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

Yes. A polynomial multiplying by a polynomial will always have a multi-termed product. Hope this helps!

Clouser

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

It is called the property of "closure".

Closure

### Is it always true that the zeros of the derivative and the zeros of the polynomial always alternate in location along the horizontal axis?

A zero of the derivative will always appear between two zeroes of the polynomial. However, they do not always alternate. Sometimes two or more zeroes of the derivative will occur between two zeroes of a polynomial. This is often seen with quartic or quintic polynomials (polynomials with the highest exponent of 4th or 5th power).

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

That property is called CLOSURE.

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

Let's try an example:The difference between (6x3 + x2 - 4x + 9) and (6x3 + x2 - 4x + 7) is 2 .2 is a polynomial of degree 0, so this example would appear to support the hypothesis in the question.However, polynomials cannot include negative exponents. So, (2x)/(2x2) produces 1/x, which is not a polynomial.So no, not always.

### Will the sum of two polynomials always be a polynomial?

Yes. Note that specifically, the sum might be a constant (just a number), or even zero, but it is convenient to include those in the definition of "polynomial".

### What does it mean for a polynomial to be closed under addition subtraction and multiplication?

It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.