Explanation Procedure used: Synthetic Division: Divide the polynomial by x − c : 1. Arrange the polynomial in descending powers, write 0 as coefficient of missing terms in the dividend. 2. Write c for the divisor x − c . 3. Bring down the leading coefficient of the dividend on the bottom row. 4. Multiply c times the value just written on the bottom row. Write the product in the next column in the second row. 5. Add the values in this new column, writing the sum in the bottom row and so on. 6. Use the numbers in the last row to write the quotient. The degree of the quotient is one less than the degree of the dividend. The last number in this row is the remainder”. Result used: If a is the zero of a polynomial function f ( x ) , then f ( a ) = 0 . Calculation: Consider the polynomial function g ( x ) = x 3 − 4 x 2 + 4 x − 16 . Check whether the value of g ( i ) is 0 or not, in order to check that the number i is a zero of the polynomial function or not. i 1 − 4 4 − 16 i − 4 i − 1 3 i + 4 _ 1 − 4 + i 3 − 4 i − 12 + 3 i From the above synthetic division, g ( i ) = − 12 + 3 i

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ISBN: 9780134210261

Author: BITTINGER, Marvin L.

Publisher: Pearson,

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Chapter 4.3, Problem 35E

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Whether the numbers i and –2i are zeros of the polynomial function g(x)=x3−4x2+4x−16 by using synthetic division.

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Chapter 4.3, Problem 34E

Chapter 4.3, Problem 36E

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Whether the numbers i and –2 i are zeros of the polynomial function g ( x ) = x 3 − 4 x 2 + 4 x − 16 by using synthetic division.

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Whether the numbers i and –2i are zeros of the polynomial function g(x)=x3−4x2+4x−16 by using synthetic division.

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Chapter 4 Solutions