# Synthetic Division

Document Sample

```					           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
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,

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,

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.

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