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: Divide the polynomial 2 x 3 − 3 x 2 + 8 x − 12 by 2 x + 3 as follows. The coefficient of x in the possible factor is not 1, so the factor is not of the form x − r . The divisor can be written as 2 x + 3 = 2 ( x + 3 2 ) . If 2 ( x + 3 2 ) is a factor of the function, 2 x + 3 is a factor. That is, if x = − 3 2 , the remainder is zero, then x + 3 2 is a factor of 2 x 3 − 3 x 2 + 8 x − 12 . The powers of x are in descending order, write down the coefficient of f ( x ) , write − 3 2 for the divisor x + 3 2 and place − 3 2 to the right. 2 − 3 8 − 12 − 3 2 Carry the left coefficient 2 to the bottom line and multiply it by − 3 2 , and place the product − 3 under the second coefficient − 3 of the top line and proceed in this similar manner to find the remainder

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Author: Washington

Publisher: PEARSON

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Chapter 15.1, Problem 4E

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Whether 2x+3 is a factor of 2x3−3x2+8x−12 or not by using synthetic division.

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Chapter 15.1, Problem 3E

Chapter 15.1, Problem 5E

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