Synthetic Division

Document Sample
Synthetic Division Powered By Docstoc
					           Let’s look at how to do this
               using the example:


5 x   4
            4 x  x  6   ( x  3)
                 2

     In order to use synthetic division these
            two things must happen:
#1   There must be a        #2 The divisor must
      coefficient for               have a leading
      every possible               coefficient of 1.
       power of the
         variable.
Step #1: Write the terms of the polynomial so
         the degrees are in descending order.




5x  0x  4x  x  6
    4                3               2


Since the numerator does not contain all the powers of x,
you must include a 0 for the x 3 .
   Step #2: Write the constant a of the divisor
            x- a to the left and write down the
            coefficients.


Since the divisor  x  3, then a  3


        5x    4
                  0x   3
                           4 x   2
                                       x 6
                                      
    3     5       0         4        1   6
 Step #3: Bring down the first coefficient, 5.

       3    5 0 4 1 6
            
            5
Step #4: Multiply the first coefficient by r (3*5).
      3     5     0     4 1 6
             15
            5
Step #5: After multiplying in the diagonals,
         add the column.



         Add the
         column
3   5     0    4 1 6
     15
    5 15
 Step #6: Multiply the sum, 15, by r; 15 3=15,
 and place this number under the next coefficient,
 then add the column again.


                              Add
3       5       0        4 1 6
         15 45
        5 15 41
Multiply the diagonals, add the columns.
    Step #7: Repeat the same procedure as step #6.

              Add       Add           Add       Add
              Columns   Columns       Columns   Columns

3      5     0      4            1             6
        15 45 123 372
       5 15 41 124 378
   Step #8: Write the quotient.

The numbers along the bottom are
coefficients of the power of x in
descending order, starting with the
power that is one less than that of
the dividend.
      The quotient is:

  3         2        378
5x 15x  41x 124 
                     x3

      Remember to place the
      remainder over the divisor.
Try this one:

   1) (t 3  6t 2  1)  (t  2)

      2     1 6        0         1
                  2 16 32
             1 8 16 31

                                 31
      Quotient  1t  8t  16 
                     2

                                t 2

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:0
posted:4/8/2013
language:simple
pages:11