Download Reteach Dividing Polynomials

Name
LESSON
6-3
Date
Class
Reteach
Dividing Polynomials
In arithmetic long division, you follow these steps: divide, multiply, subtract, and bring down.
Follow these same steps to use long division to divide polynomials.
Divide: 6x 2 x 8 2x 1 .
2
Step 1 Divide the first term of the dividend, 6x , by the first term of the divisor, 2x.
3x
Divide: 6x 2 2x 3x.
2
2x 1 6x x 8
2
6x 3x 4x 8
Multiply the complete divisor: 3x 2x 1 6x 2 3x.
Subtract and bring down.
Remember to use the
Step 2 Divide the first term of the difference, 4x, by the
Distributive Property
first term of the divisor, 2x.
when you subtract.
3x 2
2x 1 6x 2 x 8
6x 2 3x 4x 8
4x 2 10
Multiply: 3x 2x 1 6x 3x.
Divide: 4x 2x 2.
Multiply the complete divisor: 2 2x 1 4x 2.
Subtract. Use the Distributive Property.
2
Step 3 Write the quotient including the remainder.
10
6x 2 x 8 2x 1 3x 2 ______
2x 1
Use long division to divide.
4x
1.
2
x 2 4x 7x 6
2. x 4 2x 2 9x 9
4x 2 8x x 6
8
4x 1 _____
x2
5
2x 1 _____
x4
3. x 5 3x 2 5x 50
4. 3x 2 6x 2 7x 6
8
2x 1 ______
3x 2
3x 10
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c06-3_rt.indd 22
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Holt Algebra 2
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Process Black
Name
LESSON
6-3
Date
Class
Reteach
Dividing Polynomials (continued)
When the divisor is in the form (x a), use synthetic division to divide.
2
Divide: (2x x 10) (x 3).
Step 1 Find a. The divisor is (x 3). So, a 3.
Step 2 Write a in the upper left corner.
Then write the coefficients of the dividend.
3 2 1 10
2, 1, and 10 are the coefficients of 2x 2 x 10.
Step 3 Draw a horizontal line. Copy the first coefficient below the line.
3 2 1 10
2
Step 4 Multiply the first coefficient by a, or 3. Write the product in the second column. Add
the numbers in the column.
3 2 1 10
2a 2 3 6
6
2
5
Step 5 Multiply that sum by a, or 3. Write the product in the third column.
Add the numbers in the column.
Draw a box around the last number. It is the remainder.
3 2 1 10
2
Step 6
6
15
5
5
5a 5 3 15
The numbers in the bottom row are
the coefficients of the quotient.
5
Write the quotient. 2x 5 _____
x3
Use synthetic division to divide.
5. (4x 2 7x 10) (x 2)
6. (2x 2 6x 12) (x 5)
a 2
2 4
5
a
7
10
2
6 12
8
4
8
2x 4 _____
x5
12
4x 1 _____
x2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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