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Contents
Evaluation of Algebraic Expression
Factorisation of Quadratic Polynomials
Long Division
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Long
Division
This is a method
used in arithmetic and polynomial division.
First, we'll take a
look at an example of division in arithmetic.
To divide 132 by
11, we can do it like below:
12 11 )132 11 22 22
The steps taken above can also be shown in a different way when we write 132 = 102+ 3 x 10 + 2 = 100 + 30 + 2. 11 can be written as 10 + 1. The division will be as follows: 10 + 2 10 + 1 )100 + 30 + 2 100 + 10 20 + 2 20 + 2
If we substitute x= 10, we will have:
x + 2 x + 1 )x2 + 3x + 2 x2 + x 2x + 2 2x + 2
We call (x + 1) the divisor, (x2 + 3x + 2) the dividend and (x + 2) the quotient.
Thus, when division is exact,
dividend = divisor x quotient.
Example:
(6x2 - 7x - 9)/ (2x + 3)
3x - 8 2x + 3 )6x2 - 7x - 9 6x2 + 9x -16x - 9 -16x - 24 15
In this case, we cannot get an exact answer when the the dividend is divided by the divisor. What is left behind (15) is known as the remainder. Thus we have
(6x2 - 7x - 9) = (2x + 3)(3x - 8) + 15
Thus, in any division,
dividend = divisor x quotient + remainder
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