## SYNTHETIC DIVISION

Synthetic division is a short cut method of polynomial division. The condition to be used this method is, the divisor must of be of first degree and should be in the form (x-a)

Let us learn the this method through an example:

#### Divide the following polynomial using Synthetic division :

x³-6x²+12x-8 by (x-2)

Procedure:

Step 1:

Write only the coefficients of dividend in the upside division symbol, leaving enough space to write the next row.

here the divisor is x-2, so the zero is 2

put the zero 2 at the left.

(Note: In case some powers of x are left in the polynomial, then we have to write 0 for their coefficients)

Step 2:

Take the first number inside which is representing the leading coefficient, carry it down below the division symbol, without changing it.

Step 3:

Multiply the carry down value by the zero and carry up the result into the next column.Here we have to multiply 2 by 1.So that we will get 2.

Step 4:

Add down the column.Here we have -6 and 2.If we simplify this we will get -4

Step 5:

Multiply the previous carry down value with the zero and carry the result up to the next column.Here we are multiplying 2 by -4.So that we got -8.

Step 6:

Add down the column.Now we have to simplify 12 with -8.So that we are getting 4.

Step 7:

Like step 5 multiply the carry down number with zero and write in the next column.

Step 8: Add down the column. The last carry down value is the remainder. Here we got the remainder as 0. So 2 is the zero of the given polynomial. If we get any other number than 0, then that number is the remainder

So here the quotient is 1x²-4x+4 and the remainder is 0

These are the example in the topic Synthetic division.

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### Quote on Mathematics

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Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are: