The document reviews the steps for long division of polynomials. It begins by defining key terms like dividend, divisor, and remainder. It then outlines the step-by-step process for long division which includes: dividing the first term of the numerator by the first term of the denominator and placing the result in the answer; multiplying the denominator by that result and placing it below the numerator; subtracting to create a new polynomial; and repeating the process with the new polynomial. Several examples are provided to demonstrate how to perform long division of polynomials.
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2. REVIEW OF LONG DIVISION
FOR NUMBERS
Let's see how it is done with:
2
46
•The number which divides the other number is
called the divisor
•The number to be divided into is called
the dividend
Dividend Divisor
3. And here we go:
6
4
2
The first digit of the dividend (4) is divided by
the divisor.
The whole number result is placed at the top. Any
remainders are ignored at this point.
The answer from the first operation
is multiplied by the divisor. The result is placed
under the number divided into.
2
4
Now we subtract the bottom number from the top
number.
0
3
6
6
0
Bring down the next digit of the dividend.
4. Long Division
2
2
3
2
x
x
x
Write it down neatly: 1. the denominator goes first,
3. then the numerator with a line above
2. then a ")",
2
3
2 2
x
x
x
Both polynomials should have the "higher
order" terms first (those with the
largest exponents, like the "2" in x2).
5. Divide the first term of the numerator by the first term of the
denominator, and put that in the answer.
Long Division
Multiply the denominator by that answer, put that below the
numerator
Subtract to create a new polynomial
Repeat, using the new polynomial
S
t
e
p
s
7. EXAMPLE
Given:
3
4
5
27
36
18
9 x
x
x
x
4
2x
Divide the first term of the numerator by
the first term of the denominator, and put
that in the answer.
5
18x
Multiply the denominator by that answer, put
that below the numerator
Subtract to create a new polynomial
Repeat, using the new polynomial
0
3
4x
4
36x
0
4
36x
3
27x
3
27x
2
3x
2
3
4
3
4
2 x
x
x
8. EXAMPLE
Given:
3
4
5
2
45
9
9
9 x
x
x
x
3
x
Divide the first term of the numerator by
the first term of the denominator, and put
that in the answer.
5
9x
Multiply the denominator by that answer, put
that below the numerator
Subtract to create a new polynomial
Repeat, using the new polynomial
0
2
x
4
9x
0
4
9x
3
45x
3
45x
x
5
x
x
x 5
2
3
9. EXAMPLE
Given:
1
2
1 2
x
x
x
x
Divide the first term of the numerator by
the first term of the denominator, and put
that in the answer.
2
x
Multiply the denominator by that answer, put
that below the numerator
Subtract to create a new polynomial
Repeat, using the new polynomial
0
1
x
0
x
1
x
x
1
1
0
10. EXAMPLE
Given:
36
2
5 2
x
x
x
x
Divide the first term of the numerator by
thefirst term of the denominator, and put
that in the answer.
2
x
Multiply the denominator by that answer, put
that below the numerator
Subtract to create a new polynomial
Repeat, using the new polynomial
0
7
x
7
0
x
7
5
1
7
x
x
x
5
36
35
1
5
1
x
11. 36
13
10
9 2
3
x
x
x
x
EXAMPLE
Given: 2
x
Divide the first term of the numerator by
the first term of the denominator, and put
that in the answer.
3
x
Multiply the denominator by that answer, put
that below the numerator
Subtract to create a new polynomial
Repeat, using the new polynomial
0 2
x
0
2
x
4
2
x
x
2
9x
x
13
x
9
x
4
4
36
x
36
x
4
36
14. .
1
.
2
.
3
.
4
.
5
Problems
Answers to Let's Practice Division of Polynomials
2
3
4
3
6
2 x
x
x
y
y
y
2
3
2
x
5
25
7
x
x
4
x
x
x
x
x
8
24
48
16 3
4
5
2
3
4
5
y
y
y
y
5
10
12
2
x
x
x
2
4
4
2
x
x
x
5
20
9
2
x
x
x
