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 1 2 is zero of f ( x ) , then x − 1 2 is factor of f ( x ) and f ( 1 2 ) = 0 . Find the remainder of 2 x 3 + 13 x 2 + 10 x − 4 . If the remainder is zero while dividing 2 x 3 + 13 x 2 + 10 x − 4 by x − 1 2 , then 1 2 is zero of 2 x 3 + 13 x 2 + 10 x − 4 . Divide the polynomial 2 x 3 + 13 x 2 + 10 x − 4 by x − 1 2 as follows. The powers of x are in descending order, write down the coefficient of f ( x ) and zeros are inserted for missing powers, write 1 2 for the divisor x − 1 2 and place 1 2 to the right. 2 13 10 − 4 1 2 Carry the left coefficient 2 to the bottom line and multiply it by 1 2 , and place the product 1 under the second coefficient 13 of the top line

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Chapter 15.1, Problem 44E

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Whether 12 is zero of 2x3+13x2+10x−4 or not by using synthetic division.

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Chapter 15.1, Problem 43E

Chapter 15.1, Problem 45E

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