0
What else can I help you with?
What operations are polynomials closed under?
+,-,X only
Are polynomial expressions closed under multiplication?
Yes, because there is no way of multiplying two polynomials to get something that isn't a polynomial.
What operations are irrational numbers closed under?
None.
Which operation between two polynomials will not always result in a polynomial?
Division of one polynomial by another one.
How polynomials and non polynomials are alike?
they have variable
Are polynomials closed under the operations of subtraction addition and multiplication?
Yes, polynomials are closed under the operations of addition, subtraction, and multiplication. This means that when you add, subtract, or multiply two polynomials, the result is always another polynomial. For example, if ( p(x) ) and ( q(x) ) are polynomials, then ( p(x) + q(x) ), ( p(x) - q(x) ), and ( p(x) \cdot q(x) ) are all polynomials as well. However, polynomials are not closed under division, as dividing one polynomial by another can result in a non-polynomial expression.
What operations are polynomials closed under?
+,-,X only
What does it mean for a polynomial to be closed under addition subtraction and multiplication?
It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.
Are polynomials a closed set under addition?
Yes, polynomials are a closed set under addition. This means that if you take any two polynomials and add them together, the result will also be a polynomial. The sum of two polynomials retains the structure of a polynomial, as it still consists of terms with non-negative integer exponents and real (or complex) coefficients.
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.
How the polynomials and non polynomials alike?
In my opinion the question is poorly defined, since "non-polynomial" could be just about anything.
How do you make working model of maths on polynomials?
Polynomials are the simplest class of mathematical expressions. The expression is constructed from variables and constants, using only the operations of addition, subtraction, multiplication and non-negative integer exponents.
Are polynomial expressions closed under multiplication?
Yes, because there is no way of multiplying two polynomials to get something that isn't a polynomial.
Polynomials have factors that are?
Other polynomials of the same, or lower, order.
How alike polonomials and non-polynomials?
"Non-polynomials" may be just about anything; how alike or different they are will depend on what specific restrictions you put on such functions, or whether you are even talking about functions.
What operations are irrational numbers closed under?
None.
What operations are natural numbers closed?
Addition and multiplication.
