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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.
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 is the product of the polynomials?
To find the product of two polynomials, you multiply each term of the first polynomial by each term of the second polynomial and then combine like terms. For example, if you have two polynomials, (A(x) = ax^2 + bx + c) and (B(x) = dx + e), the product (P(x) = A(x) \cdot B(x)) results in (P(x) = (ax^2)(dx) + (ax^2)(e) + (bx)(dx) + (bx)(e) + (c)(dx) + (c)(e)). Finally, you simplify by combining any like terms to obtain the final expression.
Is the product of two negative integers always negative?
That is false. The product of two negative integers is always positive.
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 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 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.
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.
What is a polynomial that cannot be written as a product of two polynomials?
prime
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.
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 subtraction says hat the difference of two polynomials is always a polynomial?
Closure
To find the product of two polynomials multiply the top polynomial by each of the bottom polynomial?
(b+8)(b+8)
Which property of polynomial addition says that the sum of two polynomials is always a polynomial?
It is called the property of "closure".
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).
