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:
x³-6x²+12x-8 by (x-2)
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)
Take the first number inside which is representing the leading coefficient, carry it down below the division symbol, without changing it.
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.
Add down the column.Here we have -6 and 2.If we simplify this we will get -4
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.
Add down the column.Now we have to simplify 12 with -8.So that we are getting 4.
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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Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:
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Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?
Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”