Dividing Polynomials Using Long Division
Model Problems:
Example 1: Divide
2
2982
23
x
xxx
using long division.
29822
23
xxxx
x – 2 is called the divisor and
2982
23
xxx
is called the dividend. The first step is to find
what we need to multiply the first term of the divisor (x) by to obtain the first term of the
dividend (2x
3
). This is 2x
2
. We then multiply x – 2 by 2x
2
and put this expression underneath the
dividend. The term 2x
2
is part of the quotient, and is put on top of the horizontal line (above the
8x
2
). We then subtract 2x
3
- 4x
2
from 2x
3
– 8x
2
+ 9x – 2.
2x
2
294
)42(
29822
2
23
23
xx
xx
xxxx
The same procedure is continued until an expression of lower degree than the divisor is obtained.
This is called the remainder.
0
)2(
2
)84(
294
)42(-
29822
1 4x -2
2
2
23
23
2
x
x
xx
xx
xx
xxxx
x
We’ve found that
142
2
2982
2
23
xx
x
xxx
Example 2:
Since the dividend (the numerator) doesn’t have a second-degree term, it is useful to use placeholders so
that we do our subtraction correctly. The problem works out as follows:
Dividing we get: 4t
2
0
PRACTICE:
1.
3
31153
23
x
xxx
2.
12
41064
23
x
xxx
3.
1
1
3
x
x
ANSWERS:
1.
143
2
xx
2.
12
1
34
2
2
x
xx
3.
1
2
1
2
x
xx
