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 f ( x ) = x 6 − 35 x 4 + 259 x 2 − 225 . Check whether the value of f ( − 1 ) is 0 or not, in order to check that the number − 1 is a zero of the polynomial function or not. − 1 1 0 − 35 0 259 0 − 225 − 1 1 34 − 34 − 225 225 _ 1 − 1 − 34 34 225 − 225 0 From the above synthetic division, f ( − 1 ) = 0

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter 4, Problem 22MC

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Whether the numbers −1 and 5 are zeros of the polynomial function f(x)=x6−35x4+259x2−225 by using synthetic division.

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Chapter 4, Problem 21MC

Chapter 4, Problem 23MC

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College Algebra: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

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Whether the numbers − 1 and 5 are zeros of the polynomial function f ( x ) = x 6 − 35 x 4 + 259 x 2 − 225 by using synthetic division.

Solution Summary: The author calculates whether the numbers -1and5 are zeros of the polynomial function by using synthetic division.

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Whether the numbers −1 and 5 are zeros of the polynomial function f(x)=x6−35x4+259x2−225 by using synthetic division.

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