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 4 p 4 − p 2 − 18 p + 9 = 0 . The powers of p are in descending order, write down the coefficient of f ( p ) = 4 p 4 − p 2 − 18 p + 9 and zeros are inserted for missing powers and then place 1 to the right end. 4 0 − 1 − 18 9 1 2 Bring down the left coefficient 4 to the bottom line and multiply it by 1 2 , and place the product value 2 under the second coefficient 0 of the top line. Proceed in this similar manner, to find the quotient and remainder. 4 0 − 1 − 18 9 1 2 2 1 0 − 9 _ 4 2 0 − 18 0 3 2 [ ∵ r 2 = 3 2 also a root ] 6 12 18 0 _ 4 8 12 0 0 The numbers presented in the last row denotes the coefficients of the quotient and the remainder

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Chapter 15, Problem 29RE

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The remaining roots of the equation 4p4−p2−18p+9=0 using synthetic division.

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Chapter 15, Problem 28RE

Chapter 15, Problem 30RE

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The remaining roots of the equation 4 p 4 − p 2 − 18 p + 9 = 0 using synthetic division.

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The remaining roots of the equation 4p4−p2−18p+9=0 using synthetic division.

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Chapter 15 Solutions