LONG DIVISION

SOLVING LONG DIVISIONS!!!

Hello everyone, my name is Shubham. The one who sits next to Vincent, the guy who picked me up today to scribe next. I told you to choose a number instead of choosing me, but you choose me. At that time i was going to kill you for choosing me, but never mind :)

 So today i am gonna discuss, what i have learned in Mr. P's class today. which is to solve Long Divisions. 

There are two methods of solving long divisions:-

1. The normal division method which is a bit time consuming.

2. Synthetic Division method which is quite easy and saves our time. 

The result of division of a polynomial in x, P(x), by a binomial of the form P(x) = Q(x)+ R 

                                                                                                                         x-a               x-a

                                                          

=> NORMAL DIVISION METHOD

Example: divide  8x²+9x+3x³ -2 by x+2

Steps:

  1. write the dividend and divisor polynomial in descending powers.

       3x³+8x²+3x

2. Divide the leading term of the dividend by first term.

       3x³  = 3x²

        x

3. Multiple the divisor by newly formed term of the quotient using the distributive law and subtract the result.

                                                           3x² + 2x -1                    

                                             x+2   ) 3x³+8x²+3x-2

                                                      -    3x³+6x²

                                                                   2x²+3x

                                                                   2x²+4x

                                                                          -x -2

                                                                          -x -2

                                                                                 0

  factors = (x+2)(3x-x)(x+1)

                             

=> SYNTHETIC DIVISION

    Example: Divide 3x⁴ - 5x² - 4x + 4  by x+2

     

   Solution: P(x)= 0  =>  x+3=0 =>  x= -2

                    x-a     

Now divide all the coefficients by 3. And if any coefficient of power of x is missing in the         followings the let that coefficient be ZERO

like in this example the coefficient of x³ is missing then let that coefficient of x³  be zero

                                                                             

                                      -2  ) 2  +0  -5  +4  +  4

                                           +      -4   8   -6    -4

                                               2  -4   3   -2     0

Factor => 2x³-4x² +3x -2

The key steps of synthetic division are as follows:-

1. Arrange the coefficient of f(x) in the order of descending power of x

2. After writing the divisor in the form x-a, use "a" to generate the 2nd and 3rd rows of number as follow

3. Bring down the 1st coefficient of the dividend and multiple by "a" 

4. Then add the product to the 2nd coefficient of dividend.Repeat the process until a product is added to the constant term of (x).

Well, those are the ways Mr. P taught us in class to solve these long divisions and I hope all the readers of this blog will like amd take help of it to solve the questions.:)