To determine To discuss: Whether the number 6 is a zero of the polynomial P ( x ) = − 2 x 6 + 5 x 4 − 3 x 2 + 270 using synthetic substitution. Explanation Given: The polynomial is P ( x ) = − 2 x 6 + 5 x 4 − 3 x 2 + 270 and the number is 6 . Calculation: In the synthetic substitution method, take the coefficients of the polynomial in the descending powers of variable and if any term is missing, use a zero in that place to act as a placeholder. Since there is no term of x 5 , x 3 and x , add the value 0 x 5 + 0 x 3 + 0 x in the expression to obtain it as − 2 x 6 + 0 x 5 + 5 x 4 + 0 x 3 − 3 x 2 + 0 x + 270 . Arrange the coefficients in descending and write the values in the form as shown below: 6 − 2 0 5 0 − 3 0 270 Bring down the first coefficient of expression and then multiply it with the given number to get 6 ( − 2 ) = − 2 6 . 6 − 2 0 5 0 − 3 0 270 ↓ − 2 6 _ − 2 Now, add 0 and − 2 6 to obtain − 2 6 . 6 − 2 0 5 0 − 3 0 270 ↓ − 2 6 _ − 2 − 2 6 The obtained value is again multiplied with the given number to get 6 ( − 2 6 ) = − 12 . 6 − 2 0 5 0 − 3 0 270 ↓ − 2 6 − 12 _ − 2 − 2 6 Add 5 and − 12 to obtain − 7 . 6 − 2 0 5 0 − 3 0 270 ↓ − 2 6 − 12 _ − 2 − 2 6 − 7 The obtained value is again multiplied with the given number to get 6 ( − 7 ) = − 7 6 . 6 − 2 0 5 0 − 3 0 270 ↓ − 2 6 − 12 − 7 6 _ − 2 − 2 6 − 7 Add 0 and − 7 6 to obtain − 7 6 . 6 − 2 0 5 0 − 3 0 270 ↓ − 2 6 − 12 − 7 6 _ − 2 − 2 6 − 7 − 7 6 The obtained value is again multiplied with the given number to get 6 ( − 7 6 ) = − 42

A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

6th Edition

ISBN: 9780321900715

Author: John Hornsby, Margaret L. Lial

Publisher: PEARSON

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Chapter 3.6, Problem 53E

To determine

To discuss: Whether the number 6 is a zero of the polynomial P(x)=−2x6+5x4−3x2+270 using synthetic substitution.

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Chapter 3.6, Problem 52E

Chapter 3.6, Problem 54E

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A Graphical Approach to College Algebra, Books a la Carte Edition (6th Edition)

Ch. 3.1 - For each complex number, (a) state the real part,...Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - For each complex number, (a) state the real part,...Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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