Civil Engineering Reference
In-Depth Information
Add the columns by starting at the left. Multiply each result by
r
= 1 and
add this to the next column.
Table 1.3.
Example 1.5 Synthetic division
1
1
−
6
11
−
6
0
1
−
5
6
1
−
5
6
0
Since the remainder,
R
, is zero,
f
(
r
) = 0 and
r
= 1 is a root. The poly-
nomial can now be written as a linear equation,
x
-
r
or
x
- 1, and
the resulting reduced polynomial with coefficient of the resultants as
follows:
(
)
−+
(
)
=
3
2
2
x
−+−= −
616 1
x
x
x
x
5 60
x
Use the quadratic equation to reduce the remaining polynomial as follows:
=
−
()
±
()
−
()
()
2
5
5
416
x
bbac
a
=
−± −
2
4
51
2
±
=
=
23
,
2
21
If the remaining polynomial was divided by
x
- 2,
r
= 2 is a root as
follows:
Table 1.4.
Example 1.5 Synthetic division
2
1
−
5
6
0
2
−
6
1
−
3
0
Since the remainder,
R
, is zero,
f
(2) = 0
and
r
=
2 is a root. The resulting
polynomial is
x
- 3,
thus
x
=
r
is the third root. This can also be shown by
repeating division with
x -
3.
Table 1.5.
Example 1.5 Synthetic division
3
1
−
3
0
3
1
0
