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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Earn +20 ptsQ: Is the difference of two polynomials always a polynomial?
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Continue Learning about Algebra
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.
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