Division of one polynomial by another one.
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.
Clouser
Closure
That property is called CLOSURE.
The sum of two polynomials is always a polynomial. Therefore, it follows that the sum of more than two polynomials is also 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.
No. Even if the answer is zero, zero is still 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.
yes
Yes. A polynomial multiplying by a polynomial will always have a multi-termed product. Hope this helps!
Clouser
It is called the property of "closure".
Closure
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).
That property is called CLOSURE.
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.