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What are some similarities between rational functions and polynomial function?
Rational functions and polynomial functions both involve expressions made up of variables raised to non-negative integer powers. They can have similar shapes and behaviors, particularly in their graphs, where they may exhibit similar end behavior as the degree of the polynomial increases. Additionally, both types of functions can be manipulated algebraically using addition, subtraction, multiplication, and division, although rational functions can include asymptotes due to division by zero, which polynomial functions do not have. Both functions can also be analyzed using techniques such as factoring and finding roots.
Is -32 a polynomial?
No.
Is 2 a polynomial?
Yes, f(x) = 2 is a polynomial of degree 0 (because there are no x terms).
Describe a polynomial in one variable?
A polynomial has 2 or more variables. It can also have a negative exponent and a fractional exponent. It's different from a monomial.****BrandonW****
What does factor theorem mean?
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
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.
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 is a polynomial multiplication with a quotient of x 3 and a remainder of 2?
To get a quotient and a remainder, you would need to do a division, not a multiplication.
What is the title of this picture multiplying polynomial?
The title of a picture depicting the multiplication of polynomials could be "Visualizing Polynomial Multiplication." This title reflects the mathematical concept being illustrated, emphasizing the process of combining polynomial expressions through multiplication. The image may include visual aids, such as grids or area models, to enhance understanding of how polynomials interact.
If polynomial is not any number then how will you define a polynomial?
An expression made with constants, variables and exponents, which are combined using addition, subtraction and multiplication, ... but not division.
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.
Is the factor of polynomials means to rewrite it as multiplication?
Yes. Factoring a polynomial means to separate it into smaller factors, which, when multiplied together, give you the original polynomial.
Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
Why monomial is not polynomial?
In mathematics, a polynomial is a finite expression made up of variables and constants, by using the operations of addition, subtraction, multiplication. The other requirement is the the exponents bet non-negative whole number.A polynomial is the sum of two or more monomials. That is why a monomial is not a polynomial.
Can a constant be considered a polynomial?
No, a constant cannot be considered a polynomial because it is only a single term. A polynomial is defined as an expression that consists of the variables and coefficients that involves only the operations of subtraction, addition, multiplication, and the non-negative integer exponents.
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.
