Explanation Procedure used: Synthetic Division: Divide the polynomial by x − c “1. Arrange the polynomial in descending powers, with a 0 coefficient for any missing term. 2. Write c for the divisor x − c . To the right, write the coefficients of the dividend. 3. Write the leading coefficient of the dividend on the bottom row. 4. Multiply c times the value just written on the bottom row. Write the product in the next column in the second row. 5. Add the values in this new column, writing the sum in the bottom row. 6. Repeat the series of multiplication and additions until all columns are filled in. 7 Use the numbers in the last row to write the quotient, plus the remainder above the divisor. The degree of the first term of the quotient is one less than the degree of the first term of the dividend. The final value in this row is the remainder”. Calculation: Divide the polynomial x 2 − 6 x − 6 x 3 + x 4 by 6 + x as follows. Arrange the divisor 6 + x in descending order, it can be written as x − ( − 6 ) which is in the form of x − c , where c = − 6 . Step 1: Arrange the dividend x 2 − 6 x − 6 x 3 + x 4 in descending order and write 0 as coefficient of missing constant term, the dividend can be rewritten as x 4 − 6 x 3 + x 2 − 6 x + 0 . x − ( − 6 ) x 4 − 6 x 3 + x 2 − 6 x + 0 Step 2: Write –6 for the divisor x − ( − 6 ) and then write the coefficients of the dividend right of –6. − 6 1 − 6 1 − 6 0 Step 3: Bring down the leading coefficient of the dividend which is 1. − 6 1 − 6 1 − 6 0 _ 1 Step 4: Multiply the value in the bottom row which is 1 by –6 and write this product value in the next column in the second row. That is, − 6 ( 1 ) = − 6 . − 6 1 − 6 1 − 6 0 − 6 _ 1 Step 5: Add the values –6 and –6 and write this sum in the bottom row. That is, – 6 + ( − 6 ) = − 12 . − 6 1 − 6 1 − 6 0 − 6 _ 1 − 12 Step 6: Multiply the value in the bottom row which is –12 by –6 and write this product value in the next column in the second row. That is, − 6 ( − 12 ) = 72 . − 6 1 − 6 1 − 6 0 − 6 72 _ 1 − 12 Add the values 1 and 72 and write this sum in the last row. − 6 1 − 6 1 − 6 0 − 6 72 _ 1 − 12 73 Multiply the value in the bottom row which is 73 by –6 and write this product value in the next column in the second row

College Algebra Essentials (5th Edition)

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ISBN: 9780134469294

Author: Blitzer, Robert F.

Publisher: PEARSON

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Chapter 3.3, Problem 26E

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To divide: The polynomial x2−6x−6x3+x4 by 6+x using synthetic Division.

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Chapter 3.3, Problem 25E

Chapter 3.3, Problem 27E

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To divide: The polynomial x 2 − 6 x − 6 x 3 + x 4 by 6 + x using synthetic Division.

Solution Summary: The author explains how to divide the polynomial by x-c using synthetic division.

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To divide: The polynomial x2−6x−6x3+x4 by 6+x using synthetic Division.

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