0
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.
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What property of polynomial subtraction says hat the difference of two polynomials is always a polynomial?
Closure
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 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 property of polynomial subtraction says hat the difference of two polynomials is always a polynomial?
Closure
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 multiplication says that the product of two polynomials is always a polynomial?
Clouser
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!
Which property of polynomial addition says that the sum of two polynomials is always a polynomial?
It is called the property of "closure".
Which property of polynomial multiplication says that the product of two polynomials is always a polynomial?
That property is called CLOSURE.
Which operation between two polynomials will not always result in a polynomial?
Division of one polynomial by another one.
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).
What is a polynomial that cannot be written as a product of two polynomials?
prime
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".
Is two terms a polynomial if the definition says more than two terms. Is a bi-nomial not part of the set of polynomials?
Two terms is a binomial. More than two terms is a polynomial. Binomials are not part of the set of polynomials.
