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: It is given that r 1 = 3 and r 2 = − 2 are the roots of the equation 2 x 4 − 2 x 3 − 10 x 2 − 2 x − 12 = 0 which can be written as x 4 − x 3 − 5 x 2 − x − 6 = 0 . The powers of x are in descending order, write down the coefficient of f ( x ) = 2 x 4 − 2 x 3 − 10 x 2 − 2 x − 12 and zeros are inserted for missing powers and then place 1 to the right end. 1 − 1 − 5 − 1 − 6 3 Bring down the left coefficient 1 to the bottom line and multiply it by 1, and place the product value 1 under the second coefficient –10 of the top line. Proceed in this similar manner, to find the quotient and remainder. 1 − 1 − 5 − 1 − 6 3 3 6 3 6 _ 1 2 1 2 0 − 2

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Chapter 15, Problem 28RE

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The remaining roots of the equation 2x4−2x3−10x2−2x−12=0 using synthetic division.

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Chapter 15, Problem 27RE

Chapter 15, Problem 29RE

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Ch. 15.1 - Use the factor theorem to determine whether t − 2...Ch. 15.1 - Prob. 2PE Ch. 15.1 - Prob. 3PE Ch. 15.1 - Prob. 4PE Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - In Exercises 1–4, make the given changes in the...Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E

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The remaining roots of the equation 2 x 4 − 2 x 3 − 10 x 2 − 2 x − 12 = 0 using synthetic division.

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The remaining roots of the equation 2x4−2x3−10x2−2x−12=0 using synthetic division.

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Chapter 15 Solutions