# Synthetic Division Calculator: Meaning and Formulas Used

TSynthetic Division can be dubbed as the method opted for Euclidean polynomials division with small variants of calculations and writing. This particular synthetic division calculator allows the division process of any given polynomial.

## Synthetic Division Preparation

Let us take a look at the synthetic division solver and preparation process with this example given here:
3x4+5x3+2x+4/x2+2x+1

Step-1:
Negate the divisor co-efficients

Step-2:
Write the dividend co-efficients towards the top (mention zero for any missed terms)

Step-3:
Remove the highest coefficient divisor

Step-4:
Write the remainder divisor of the co-efficients in a diagonal way towards the left

### Synthetic Division Process for the Monic Divisors

3x4+5x3+2x+4/x2+2x+1
The same example can be used to show you how the monic divisors work.

Step-1:
Drop the highest co-efficient dividend in the initial column for the result row.

Step-2:
Multiply the divisor diagonal with the last value of the column in the result row.

Step-3:
Place the result of the multiplication in a diagonal flow towards the right side from the previous result column

Step-4:
Perform the addition process with the following column & write down its sum in very same column of the result row

Step-5:
Repeat the steps 2 to 4 until it goes past all the columns in the topmost row

Step-6:
Sum up the values in remaining columns & write down the results in the result row

Step-7:
Now, separate the result & remainder. The total terms in the remainder is equal to the number of the divisor terms subtracted by one.

The polynomial factoring calculator also helps factor the polynomials in proper steps which includes the binomials, trinomials, quadratics, and so on. In order to opt for the substitution calculator, the methods used include:

1. Factoring Monomials
3. Grouping
4. Regrouping
5. Square of Difference/Sum
6. Cube of Difference/Sum
7. Differences of the squares
8. Difference/sum of the cubes
9. Rational Zeros Theorem

These factoring polynomials work with the remainder theorem calculator while accepting both the multivariate and univariate polynomials. When taking a dig at the remainder theorem, here is an example that can better traverse what takes place with this polynomial.

Find f(3) for the f(x) = x3-x2+2x+7
According to remainder theorem, the f(a) polynomial here is a remainder from the division of f(x) by the polynomial x-a.
Thus, in order to find the value for f(3), you need to obtain the remainder by dividing xk3-x2+2x+7 by x-3 The use of remainder theorem calculator gets you the 31 as the remainder.
This is why, the value of f (3) =31