# Need to find:under what circumstances can synthetic division are used to divide polynomial.

Question
Polynomial division
Need to find:under what circumstances can synthetic division are used to divide polynomial.

2021-02-13
Synthetic division:
In algebra synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than occur with long polynomial division.
The circumstances are:
It is mostly used for division by binomials of the form x — a, but the method generalized to division by any monic polynomial.
It is dividing for the linear factor.
It can be used to divide polynomial polynomials when the division is the binomial of the form x—c and cis a constant.

### Relevant Questions

The condition under which we may use synthetic division to divide polynomials
Synthetic division is a process for dividing a polynomial by x - c.
The coefficient of x in the divisor is 1.
How might synthetic division be used if you are dividing by $$2x - 4$$?
Whether the statement “When performing the division $$\frac{x^{5} +1}{x + 1}$$ there's no need for me to follow all the steps involved in polynomial long division because I can work the problem in my head and see that the quotient must be $$x^{4} + 1$$ ”makes sense or not.” Makes sense or not.
How can the division algorithm be used to check the result of the polynomial division.
How the division algorithm can be used to check the result of the polynomial division.
Whether the division of polynomial $$\frac{3x^{4}-x+1}{x-5}$$ using synthetic division method is directly possible or not.
Synthetic division is a shortcut process for polynomial division.
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $$\frac{x^{n}-1}{x-1}$$.
$$\frac{x^{4}-1}{x-1}$$
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $$\frac{x^{n}-1}{x-1}$$.
$$\frac{x^{3}-1}{x-1}$$
Writing Complete each polynomial division. Write a brief description of the pattern that you obtain, and use your result to find a formula for the polynomial division $$\frac{x^{n}-1}{x-1}$$.
$$\frac{x^{2}-1}{x-1} =$$ ?