Division, Mathematics

Assignment Help:

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.)


Related Discussions:- Division

How much does it car cost her per year, Ashley's car insurance costs her $1...

Ashley's car insurance costs her $115 per month. How much does it cost her per year? Multiply $115 by 12 because there are 12 months in a year; $115 × $12 = $1,380 per year.

Área de un rectangulo, calcula el área de la región sombreada de un rectáng...

calcula el área de la región sombreada de un rectángulo cuya base es 12.6 cm y su altura es 8.4

Determine the projection - vector, Determine the Projection of b = (2, 1, -...

Determine the Projection of b = (2, 1, -1) onto a = (1, 0, -2) There is a requirement of a dot product and the magnitude of a. a →  • b → = 4                             ||a

Geometry, what is the product of the solutions to the equation: x2+4x=-4

what is the product of the solutions to the equation: x2+4x=-4

Solving equations by completing the square method, I need help for Solving ...

I need help for Solving Equations by Completing the Square Method, can anybody help me out for this?

Chp 8 Study, Center and Radius 1)(x+2)^2-(y-3)^2=4

Center and Radius 1)(x+2)^2-(y-3)^2=4

An initial species population , An initial species population is y(0) = 300...

An initial species population is y(0) = 3000. At t=0 the population starts to grow exponentially with a doubling time of 2 years. Mark the only correct statement: a)    The per

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd