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Q: Will the product of two polynomials always be a polynomials?
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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!


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

Clouser


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

That property is called CLOSURE.


What is a polynomial that cannot be written as a product of two polynomials?

prime


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.


Is it possible to add 2 polynomials together and your answer is not a polynomial?

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


What property of polynomial subtraction says hat the difference of two polynomials is always a polynomial?

Closure


To find the product of two polynomials multiply the top polynomial by each of the bottom polynomial?

(b+8)(b+8)


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

It is called the property of "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 operation between two polynomials will not always result in a polynomial?

Division of one polynomial by another one.


Can you always use synthetic division for dividing polynomials?

no