Division, Mathematics

Before taking up division of polynomials, let us acquaint ourselves with some basics. Suppose we are asked to divide 16 by 2. We know that on dividing 16 by 2 we get 8. In mathematics we call 16, 2 and 8 by specific names. 16 is called dividend, 2 is called the divisor and 8 is the quotient. However, it is not always that we get an integer like 8 when we divide a number by another. For instance, divide 9 by 2. In addition to the dividend (9), divisor (2) and quotient (4) we are left with another term 1. This is referred to as the remainder. When the dividend is not exactly divisible by the divisor we get a remainder. We find these terms even when one expression is divided by another. Also we follow these rules.

  1. We arrange the terms of the divisor and the dividend in ascending or descending powers of some common letter. Ascending order refers to arranging terms from lower power to higher powers and descending orders refers to opposite of this. Usually we write them in the descending order.

  2. Divide the term on the left of the dividend by the term left of the divisor and put the result in the quotient.

  3. Multiply the whole divisor by this number (quotient) and put the resultant product under the dividend.

  4. Subtract the product from the dividend and bring down the required number of terms as may be deemed necessary.

  5. Repeat this procedure until all the terms in the dividend have been brought down.

We understand this with the help of a couple of examples.

Example 

Divide x2 + 4x + 4 by x + 2.

We find that the terms of the dividend (x2 + 4x + 4) and the divisor (x + 2) are already in the descending order. The left most term in the dividend is x2, while in the divisor it is x. We find the quotient as

629_division.png

We multiply the divisor x + 2 with this quotient x. We get x2 + 2x. We write this under the dividend as shown.

Others

  x + 2 )

x2 + 4x + 4

( x + 2

 

 (-)

x2 + 2x 

 


 

 

         2x + 4

 

 

 

(-)    2x + 4  

 


 

 

                 0

 


On subtracting x2 + 2x from the dividend we obtain 2x + 4. (x2 + 4x + 4 - (x2 + 2x)    = x2 + 4x + 4 - x2 - 2x). We write this expression as shown above.

At this stage, we take the left most quantity of the difference (dividend - product) and that of the divisor and obtain their quotient. It will be 

2029_division1.png

Since the sign of the quotient is positive we write it as shown. Then we multiply x + 2 with 2. That will be 2x + 4. We write under the difference got earlier and subtract it from the difference. We get 2x + 4 - (2x + 4) = 2x + 4 - 2x - 4 = 0. This is shown in the example above. Since the dividend is exactly divisible by the divisor the remainder is zero.

After solving this problem can we say that x + 2 is a factor of x2 + 4x + 4? Of course we can. As we write 8 = 2.4 or 1.8, we can write

                            x2 + 4x + 4 = (x + 2)(x + 2)

(Note: Division of expressions where some of the terms are fractions is also carried out in the same manner we have seen above.)

Posted Date: 9/13/2012 3:15:49 AM | Location : United States







Related Discussions:- Division, Assignment Help, Ask Question on Division, Get Answer, Expert's Help, Division Discussions

Write discussion on Division
Your posts are moderated
Related Questions
Does this Point Lie on The Line? How do you know if a point lies on a given line? For example, does the point (1, 2) lie on the line 3x + y = 7? If you graph the line and the

how to find the sum of the measure of the interior angles of each convex polygon

which ratio is largar. 1. 15:16 or 24:25

A Stone is dropped from the top of the tower and travel 24.5 m in last second of its journey. the height of the tower is ...?

The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field

Q. Difference between Probability and statistics? Ans. Probability and statistics are used in many different aspects of life. What are they and why are they so popular?

THE PREREQUISITES FOR MULTIPLICATION : The word 'multiply', used in ordinary language, bears the meaning 'increase enormously For instance, bacteria multiply in favourable conditi

What is the Magna Carta

A professor is interested in decisive if attending college influences the level at which an individual cooperates with the police. The professor is not sure  if attending college w

Interpretation A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that there is a causal relationship that is