Explanation Given: The given polynomial equation is x 3 − 6 x 2 + 7 x + 2 = 0 and the partial solution set is { 2 } . Theorem used: Factor theorem: If P ( x ) is a polynomial function and r is any number, then If P ( r ) = 0 , then x − r is a factor of P ( x ) . If x − r is a factor of P ( x ) , then P ( r ) = 0 . 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: Let P ( x ) = x 3 − 6 x 2 + 7 x + 2 Given that 2 is the solution of P ( x ) = 0 . Hence 2 is the zero of P ( x ) . Now let us use synthetic division and divide P ( x ) by x − 2 , to obtain a reminder of 0. Now write the coefficients of the dividend with its terms in descending power of x , and 2 from the divisor in the following form. 2 1 − 6 7 2 Then we follow the following steps. 2 1 − 6 7 2 1 (Bring down 1) Now, multiply 2 and 1 together to get 2, and add − 6 and 2 to get − 4 . 2 1 − 6 7 2 2 1 − 4 Now, multiply 2 and − 4 together to get − 8 , and add 7 and − 8 to get − 1 . 2 1 − 6 7 2 2 − 8 1 − 4 − 1 Now, multiply 2 and − 1 together to get − 2 , and add 2 and − 2 to get 0

12th Edition

ISBN: 9781305652231

Author: R. David Gustafson, Jeff Hughes

Publisher: Cengage Learning

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Chapter 4.3, Problem 85E

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To find:

The complete solution set of the polynomial equation, whose partial solution set is also given as x3−6x2+7x+2=0;{2}.

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Chapter 4.3, Problem 84E

Chapter 4.3, Problem 86E

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The complete solution set of the polynomial equation, whose partial solution set is also given as x 3 − 6 x 2 + 7 x + 2 = 0 ; { 2 } .

Solution Summary: The author explains that the complete solution set of the polynomial equation is left2right.

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To find:

The complete solution set of the polynomial equation, whose partial solution set is also given as x3−6x2+7x+2=0;{2}.

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Chapter 4 Solutions

The complete solution set of the polynomial equation, whose partial solution set is also given as x 3 − 6 x 2 + 7 x + 2 = 0 ; { 2 } .

Solution Summary: The author explains that the complete solution set of the polynomial equation is left2right.

Concept explainers

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To find: The complete solution set of the polynomial equation, whose partial solution set is also given as x3−6x2+7x+2=0;{2}.

Want to see the full answer?

Chapter 4 Solutions

To find:

The complete solution set of the polynomial equation, whose partial solution set is also given as x3−6x2+7x+2=0;{2}.