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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 22 Holt Algebra 2 12/29/05 8:30:48 PM 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. 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