Synthetic Division Method

Synthetic Division is a systematic approach to solve a problem. For solving a question you need to identify the divisor and consider the coefficients of the polynomial. Perform synthetic division and then derive the solution for the same. This method involves a set of basic arithmetic operations and this makes it an easy way to solve the problem when compared to the traditional method for division.

How to do Synthetic Division?

Below will be step-by-step solution for the division of any linear polynomial with the help of synthetic division method.

Let us consider the previous example only and solve it step by step i.e. dividing 4x² – 6x -8 by x – 2.

Step 1: Identifying Co-Efficient.

Write down all the coefficients including the missing term. If some term is missing write 0 in its place.

4 -6 -8

Step 2: Identify the divisor.

Here, (x-2) is divisor so x -2 =0 ⇒ x = +2. Therefore, 2 is the divisor.

2 | 4 -6 -8

Step 3: Write first co-efficient as it is.

Write down the first coefficient as it is here 4 is the first co-efficient.

Step 4: Multiply and add it with divisor.

Multiply the first coefficient with the divisor here 2*4 and write the result below second co-efficient and add it and write down the result.

Step 5: Repeat the step 4.

Step 6: Derive Result

Result will depend on the last line of the solution given above. Here, the result will be

4x + 2 – 4/(x-2)