Arrange terms in both in decreasing order based on the exponents.
Use the algorith for long division. This is just like long division.
Step 1. Divide 1st term into 1st term, (place answer above division line).
Step 2. Multiply that answer by all terms in the divisor, (place this result below the polynomial inside the division bar)
Step 3. Subtract like terms (answer goes down 1 line) and bring down another term to continue.
Repeat: Step 1. Divide 1st term into new 1st term. etc
Yes.
If you know one linear factor, then divide the polynomial by that factor. The quotient will then be a polynomial whose order (or degree) is one fewer than that of the one that you stared with. The smaller order may make it easier to factorise.
how alike the polynomial and non polynomial
A root.
13 is not a polynomial.
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.
Your dividing with variables now.
factor
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.
You can find explanation and examples here: http://en.wikipedia.org/wiki/Polynomial_division
In video example 36, the process of dividing a polynomial by a binomial is demonstrated using long division. The polynomial is divided term by term, starting with the leading term of the polynomial, and determining how many times the leading term of the binomial fits into it. This is followed by multiplying the entire binomial by that quotient term, subtracting the result from the original polynomial, and repeating the process with the remainder until the polynomial is fully divided. The final result includes both the quotient and any remainder expressed as a fraction.
There is no other name for a polynomial.
A g
The quotient in polynomial form refers to the result obtained when one polynomial is divided by another polynomial using polynomial long division or synthetic division. It expresses the division result as a polynomial, which may include a remainder expressed as a fraction of the divisor. The quotient can help simplify expressions and solve polynomial equations. For example, dividing (x^3 + 2x^2 + x + 1) by (x + 1) yields a quotient of (x^2 + x) with a remainder.
the first steps that you will have to take is gtegeagerge
To square an expression, multiply it by itself. And to multiply a polynomial by a polynomial, multiply each part of one polynomial by each part of the other polynomial.
A local minimum.