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That means that you divide one polynomial by another polynomial. Basically, if you have polynomials "A" and "B", you look for a polynomial "C" and a remainder "R", such that:
B x C + R = A
... such that the remainder has a lower degree than polynomial "B", the polynomial by which you are dividing. For example, if you divide by a polynomial of degree 3, the remainder must be of degree 2 or less.
What else can I help you with?
When will you use polynomial long division in life?
In a mathematics exam.
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.
How do nurses use polynomial division?
They don't. At least, not for their nursing work.
What are some examples in real life that you might use polynomial division?
Pharmacists and the makers of drugs use polynomial division. They use this type of division to help create formulas to make sure that the proper amount of drug is being distributed to the patients depending on the variables involved.
What are some real life examples where you would use polynomial division?
you can use it house or at the mall or anywhere
Division of polynomial by a polynomial?
Can be done.
Which operation between two polynomials will not always result in a polynomial?
Division of one polynomial by another one.
What is synthetic division?
Synthetic division is a simplified method for dividing a polynomial by a linear binomial of the form (x - c). It involves using the coefficients of the polynomial and performing operations that resemble long division but are more streamlined. This technique is particularly useful for quickly finding polynomial quotients and remainders without having to write out the entire long division process. Synthetic division is efficient and can be applied when the divisor is a linear polynomial.
How can you tell if a binomial divides evenly into a polynomial?
Do the division, and see if there is a remainder.
Why are polynomials not closed under division?
Polynomials are not closed under division because dividing one polynomial by another can result in a quotient that is not a polynomial. Specifically, when a polynomial is divided by another polynomial of a higher degree, the result can be a rational function, which includes terms with variables in the denominator. For example, dividing (x^2) by (x) gives (x), a polynomial, but dividing (x) by (x^2) results in (\frac{1}{x}), which is not a polynomial. Thus, the closure property does not hold for polynomial division.
What is an expression that completely divides a given polynomial?
An expression that completely divides a given polynomial without leaving a remainder is called a factor of the polynomial. This means that when the polynomial is divided by the factor, the result is another polynomial with no remainder. Factors of a polynomial can be found by using methods such as long division, synthetic division, or factoring techniques like grouping, GCF (greatest common factor), or special patterns.
When will you use polynomial long division in life?
In a mathematics exam.
What is the remainder when 2 is synthetically divided into the polynomial?
To find the remainder when a polynomial is divided by (x - 2) using synthetic division, we substitute (2) into the polynomial. The remainder is the value of the polynomial evaluated at (x = 2). If you provide the specific polynomial, I can calculate the remainder for you.
A remainder of zero in the process of doing synthetic division tells you that you have found a root of the polynomial function and a factor of the polynomial. A. True?
true
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.
How do nurses use polynomial division?
They don't. At least, not for their nursing work.
What is the step-by-step process of solving polynomial equations using the Ruffini method?
The Ruffini method, also known as synthetic division, is a step-by-step process for solving polynomial equations. Here is a concise explanation of the process: Write the coefficients of the polynomial equation in descending order. Identify a possible root of the polynomial equation and use synthetic division to divide the polynomial by the root. Repeat the process until the polynomial is fully factored. Use the roots obtained from the synthetic division to write the factors of the polynomial equation. Solve for the roots of the polynomial equation by setting each factor equal to zero. This method allows for the efficient solving of polynomial equations by breaking them down into simpler factors.
