In previous article, we learn the procedure of doing 'division of large numbers' with divisor's first digit as '1'. In this article, we learn the procedure with divisor's first digit has all numbers except 1.
In this article too, we first go through with division of polynomials.
-4x3-7x2+9x-12 divided by 2x-4
_________________
2x-4 | -4x3 - 7x2 + 9x - 12 | -2x2 - 15/2x - 21/2
-(-4x3 + 8x2)
------------------------
-15x2 + 9x
-(-15x2 + 30x)
------------------------
- 21x - 12
-(- 21x + 42)
---------------------
-54
Quotient = -2x2 - 15/2x - 21/2 , Remainder = -54
See the above example in another form by making the first coefficient of the divisor as '1'. Like in following example, we divide the divisor by 2 and later divide the quotient also by 2 :
2x-4 | -4x3 - 7x2 + 9x - 12
x-2
+2 - 8 - 30 - 42
-----------------------------
-4 - 15 - 21 - 54
Now, divide this by 2 (2 is the first coefficient of the divisor).
Also note that we don't divide the remainder by 2, it will remain constant.
-2 - 15/2 - 21/2 - 54
Quotient = -2x2 - 15/2x - 21/2 , Remainder = -54
One more illustration:
First, make the first coefficient of divisor as '1'
2x2 -3x +1 | 2x5 -9x4 +5x3 +16x2 -16x +36
x2-3/2x+1/2
+3/2 -1/2 3 -1
-9 +3
-15/2 +5/2
69/4 -23/4
---------------------------------------------
2 -6 -5 23/2 15/4 +121/4
Divide by 2 ) 1 -3 -5/2 23/4 15/4 +121/4
Quotient = x3-3x2-5/2x+23/4 , Remainder = 15/4x +121/4
Remember that Remainder is constant in every case
In this article too, we first go through with division of polynomials.
-4x3-7x2+9x-12 divided by 2x-4
_________________
2x-4 | -4x3 - 7x2 + 9x - 12 | -2x2 - 15/2x - 21/2
-(-4x3 + 8x2)
------------------------
-15x2 + 9x
-(-15x2 + 30x)
------------------------
- 21x - 12
-(- 21x + 42)
---------------------
-54
Quotient = -2x2 - 15/2x - 21/2 , Remainder = -54
See the above example in another form by making the first coefficient of the divisor as '1'. Like in following example, we divide the divisor by 2 and later divide the quotient also by 2 :
2x-4 | -4x3 - 7x2 + 9x - 12
x-2
+2 - 8 - 30 - 42
-----------------------------
-4 - 15 - 21 - 54
Now, divide this by 2 (2 is the first coefficient of the divisor).
Also note that we don't divide the remainder by 2, it will remain constant.
-2 - 15/2 - 21/2 - 54
Quotient = -2x2 - 15/2x - 21/2 , Remainder = -54
One more illustration:
First, make the first coefficient of divisor as '1'
2x2 -3x +1 | 2x5 -9x4 +5x3 +16x2 -16x +36
x2-3/2x+1/2
+3/2 -1/2 3 -1
-9 +3
-15/2 +5/2
69/4 -23/4
---------------------------------------------
2 -6 -5 23/2 15/4 +121/4
Divide by 2 ) 1 -3 -5/2 23/4 15/4 +121/4
Quotient = x3-3x2-5/2x+23/4 , Remainder = 15/4x +121/4
Remember that Remainder is constant in every case
