LONG DIVISION METHOD

Steps

1. The rule of LDM is :

and..

So here is an example:

Step 1

Step 2 Multiply (In this case : x^3(x-3))

Step 3 : Bring down the answer

Step 4 : subtract

Step 5 : Repeat the steps with the other Variables

Step 6 : Repetition of steps 2 -4

Final answer !

Since Dividend = Quotient x Divisor + Remainder

Things to take note of:

Dividend MUST be in

__descending index form__(x^4,x^3,x^2,x,constant)
IF the equation is similar to e.g. x^5-1 / x-3,

then the dividend used in LDM should be

( x^5 + 0x^4 + 0x^3 + 0x^2 + 0x - 1 ) / ( x - 3 )

So that dividend is arranged in descending index form

THATS ALL!!! :D

Thanks for the great notes. A few comments:

ReplyDeleteThe first and second pictures:

With reference to the divisor, what is the degree of the remainder?

The last picture:

It's kind of weird to write final answer = ...

The last 2 lines of expression are not equivalent!

Basically:

\[\begin{array}{l}{x^4} - 2{x^3} - 4{x^2} + 11x - 6 \equiv \left( {x - 3} \right)\left( {{x^3} + {x^2} - x + 8} \right) + 18\\\frac{{{x^4} - 2{x^3} - 4{x^2} + 11x - 6}}{{x - 3}} \equiv {x^3} + {x^2} - x + 8 + \frac{{18}}{{x - 3}}\end{array}\]