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.
What else can I help you with?
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.
Which property of polynomial subtraction says that the difference of two polynomials is always a polynomial?
The property that states the difference of two polynomials is always a polynomial is known as the closure property of polynomials. This property indicates that when you subtract one polynomial from another, the result remains within the set of polynomials. This is because polynomial operations (addition, subtraction, and multiplication) preserve the degree and structure of polynomials. Thus, the difference of any two polynomials will also be a polynomial.
What property of polynomial subtraction says that the difference of two polynomials is always a polynomial?
The property of polynomial subtraction that ensures the difference of two polynomials is always a polynomial is known as closure under subtraction. This property states that if you take any two polynomials, their difference will also yield a polynomial. This is because subtracting polynomials involves combining like terms, which results in a polynomial expression that adheres to the same structure as the original polynomials.
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.
Will the product of two polynomials always be a polynomial?
Yes, the product of two polynomials will always be a polynomial. This is because when you multiply two polynomials, you are essentially combining like terms and following the rules of polynomial multiplication, which results in a new polynomial with coefficients that are the products of the corresponding terms in the original polynomials. Therefore, the product of two polynomials will always be 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).
