Explanation Procedure used: Procedure for Synthetic Division: 1. Write the coefficients of f ( x ) . Be certain that the powers are in descending order and that zeros are inserted for missing powers. 2. Carry down the left coefficient, then multiply it by r , and place this product under the second coefficient of the top line. 3. Add the two numbers in the second column and place the result below. Multiply this sum by r and place the product under the third coefficient of the top line. 4. Continue this process until the bottom row has as many numbers as the top row. Calculation: If − 4 is zero of f ( r ) , then r + 4 is factor of f ( r ) and f ( − 4 ) = 0 . Find the remainder of r 4 + 5 r 3 − 18 r − 8 . If the remainder is zero when divide r 4 + 5 r 3 − 18 r − 8 by r + 4 , then − 4 is zero of r 4 + 5 r 3 − 18 r − 8 . Divide the polynomial r 4 + 5 r 3 − 18 r − 8 by r + 4 as follows. The powers of r are in descending order, write down the coefficient of f ( r ) and zeros are inserted for missing powers, write − 4 for the divisor r + 4 and place − 4 to the right. 1 5 0 − 18 − 8 − 4 Carry the left coefficient 1 to the bottom line and multiply it by − 4 , and place the product − 4 under the second coefficient 5 of the top line

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Author: Washington

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Chapter 15.1, Problem 42E

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Whether −4 is zero of r4+5r3−18r−8 or not by using synthetic division.

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Chapter 15.1, Problem 41E

Chapter 15.1, Problem 43E

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