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What else can I help you with?
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!
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.
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
Differentiate of polynomial and algebraic expression?
A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. In another polynomial is a subset of algebraic expression.
What is an inverse property of addition?
+8 - 8 = 0 is an example of the inverse property of addition. Inverse Property of Addition-A number added to its opposite integer will always equal zero. (The order does not matter, since it is addition.) [Ex. 3 + (-3) = 0 or (-3) + 3 = 0]
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.
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 multiplication says that the product of two polynomials is always a polynomial?
Clouser
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.
Is the difference of 2 polynomials always a polynomial?
yes
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!
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 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.
What operations are polynomials closed under?
+,-,X only
