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 (2x3). This is 2x2. We then multiply x – 2 by 2x2 and put this expression underneath the
dividend. The term 2x2 is part of the quotient, and is put on top of the horizontal line (above the
8x2). We then subtract 2x3 - 4x2 from 2x3 – 8x2 + 9x – 2.
2x2
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: 8𝑡3+14𝑡+8
2𝑡+1
