Explanation Given: The given polynomial function is P ( x ) = 2 x 4 − x 2 + 2 . Theorem used: Remainder theorem: If P ( x ) is a polynomial function, c is any number, and P ( x ) is divided by x − c , the remainder is P ( c ) . Calculation: Consider the given polynomial function P ( x ) = 2 x 4 − x 2 + 2 . We need to find the value of P ( − i ) using synthetic division. By Remainder theorem, when P ( x ) is divided by x + i , the remainder is P ( − i ) . Hence let us divide P ( x ) by x + i , to find the remainder. Let us use synthetic division to perform the division process. Now write the coefficients of the dividend with its terms in descending power of x , and − i from the divisor in the following form. − i 2 0 − 1 0 2 Then we follow the following steps. − i 2 0 − 1 0 2 2 (Bring down 2) Now, multiply − i and 2 together to get − 2 i , and add 0 and − 2 i to get − 2 i . − i 2 0 − 1 0 2 − 2 i 2 − 2 i Now, multiply − i and − 2 i together to get − 2 , and add − 1 and − 2 to get − 3

Bundle: College Algebra, Loose-leaf Version + WebAssign Printed Access Card for Gustafson/Hughes' College Algebra, Single-Term

12th Edition

ISBN: 9781337604642

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Chapter 4.3, Problem 58E

To determine

To find:

The value of P(−i) using synthetic division.

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Chapter 4.3, Problem 57E

Chapter 4.3, Problem 59E

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Bundle: College Algebra, Loose-leaf Version + WebAssign Printed Access Card for Gustafson/Hughes' College Algebra, Single-Term

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