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What else can I help you with?
Polynomials with the same roots always have the same graphs?
false
When you divide two fractions is the quotient always smaller than the dividend?
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!
Which property of polynomial addition says that the sum of two polynomials is always a polynomial?
It is called the property of "closure".
What is another way to divide 3 by one-sixth?
3 divided by 1/6 is the same thing as 3x6....you always flip the fraction after the division sign, and change it to multiplication when dividing fractions -sophmore in high school-
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.
Which operation between two polynomials will not always result in a polynomial?
Division of one polynomial by another one.
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.
When dividing fractions does the answer always end with an improper fraction?
Not always. There are times when division of fractions results in a non-improper fraction.
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 the difference of 2 polynomials always a polynomial?
yes
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 operations are polynomials closed under?
+,-,X only
Polynomials with the same roots always have the same graphs?
false
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.
Do you always use the property of distribution when multiplying monomials and polynomials?
Yes.
When you divide two fractions is the quotient always smaller than the dividend?
yes
