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Enter the dividend and divisor to perform synthetic division on polynomial expression.

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Use this synthetic division calculator to divide the polynomials by binomials. It processes step-by-step synthetic division to find the actual quotient and remainders.

Synthetic division is a shortcut method for dividing a polynomial by linear factors where the leading coefficient is 1. If it's not equal to 1, then it requires modifying the dividend to make the leading coefficient 1 before using the method. This method provides you with the quotient (the result of the division) and the remainder. It uses the divisors of the form "(x + a)" and "(x - a)".

- Polynomials are considered dividends
- Linear factors of the form (ax + b) are divisors

**\(\frac{P(x)}{(x-a)} =\ Q(x) + \frac{R}{(x-a)}\)**

Where:

**P(x):**Dividend Polynomial of any order**(x-a):**Linear Factor of degree “1”**Q(x):**Quotient**R:**Remainder

- Write the coefficients of the dividend in descending order
- Write zeros of linear factors as the divisor
- Convert values in the synthetic division format
- Carry down the leading coefficient in the next column
- Multiply the leading coefficient by the divisor and put in next column
- Repeat steps 4 and 5 until the last coefficient
- The value in the last column is a remainder, the number from the right is the quotient

Solve the given below values by using the synthetic division method.

- Dividend: \(\ 2x^3 - 5x^2 + 3x - 7\)
- Divisor: \(\ x - 2\)

Navigate with the steps to evalaute polynomials using synthetic division method:

\(\dfrac{2 x^{3} - 5 x^{2} + 3 x - 7}{x - 2}\)

**Step #1: Write The Coefficients Of The Dividend**

2, -5, 3, -7

**Step #2: Write Zeros Of Linear Factors As The Divisor**

x - 2 = 0

x = 2

**Step #3: Write values in synthetic division format:**

\(\begin{array}{c|rrrrr}& x^{3}&x^{2}&x^{1}&x^{0} \\2.0& 2&-5&3&-7 \\&&\\\hline&\end{array}\)

**Step #4: Carry Down The Leading Coefficient In The Next Column**

\(\begin{array}{c|rrrrr}2.0& 2&-5&3&-7 \\&&\\\hline&2\end{array}\)

**Step #5: Multiply The Leading Coefficient By The Divisor**

Using the synthetic division to find zeros, simply multiply the obtained value by the denominator and write the result into the next column.

\(\ 2 \times (2.0) = 4\)

Write The Outcome In The Next Column

\(\ \begin{array}{c|rrrrr}2.0&2&-5&3&-7\\&&4&\\\hline&2&\end{array}\)

**Step #6: Repeat Steps 4 & 5 Until The Last Coefficient**

\(\ \begin{array}{c|rrrrr}2.0&2&-5&3&-7\\&&4&-2&2&\\\hline&2&-1&1&-5&\end{array}\)

**Step #7: Value in Last Column is Remainder, The Number From Right Is Quotient **

The quotient is \(\ 2 x^{2} - x + 1\), and the remainder is \(\ {-5}\)

Therefore, the final answer is:

\(\dfrac{2 x^{3} - 5 x^{2} + 3 x - 7}{x - 2} = {2 x^{2} - x + 1 - \dfrac{5}{x - 2} }\)

**Fast & Easy Calculations:**Our calculator performs quick calculations, saving valuable time**Step-by-Step Solution:**The calculator provides you with a detailed step-by-step division of polynomials**Clear UI:**It's simple interface allows to make straight-forward calculations, no technical expertise is required

This division method is applicable when the divisor of a polynomial is a linear factor in the form ax + b, where the highest power of x is 1. For this division if you need complete calculations, take help from this synthetic division solver that simplifies the division with given steps.

No, the synthetic division method only works to divide polynomials by linear expressions (a binomial of the form x-c, in which c is represented as a constant).

The calculator only works to divide polynomials using synthetic division as we already stated above.

**References:**

Form the source of courses.lumenlearning.com: Synthetic Division.

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