Explanation Given: The polynomial f ( x ) is 2 x 3 + 3 x 2 + 2 x + 3 . Concept: Let the polynomial of the form P ( x ) = a n x n + a n − 1 x n − 1 + ......... + a 1 x + x 0 .where all the coefficients are an integer. If p and q is zero of P ( x ) , then p is a factor of a 0 and q is a factor of a n . In the given polynomial f ( x ) , the degree of the polynomial is 3, then, the distinct zeros of the polynomial f ( x ) are at most 3. The value of the a 0 is 3 and a n is 2. According to the Rational zeros theorem, the possibilities of the p q is, Possibilities of p Possibilities of q = ± 1 , ± 3 ± 1 , ± 2 The possible zeros of the polynomial f ( x ) are 1 , − 1 , 3 , − 3 , 1 2 , − 1 2 , 3 2 and − 3 2 . Let 1 is zero of the polynomial. According to the synthetic division. 1 2 3 2 3 2 5 7 2 5 7 | 10 Thus, 1 is not zero of the polynomial f ( x ) . Let − 1 is zero of the polynomial. According to the synthetic division. − 1 2 3 2 3 − 2 − 1 − 1 2 1 1 | 2 Thus, − 1 is not zero of the polynomial f ( x ) . Let 3 is zero of the polynomial. According to the synthetic division. 3 2 3 2 3 6 27 87 2 9 29 | 90 Thus, 3 is not zero of the polynomial f ( x ) . Let − 3 is zero of the polynomial. According to the synthetic division. − 3 2 3 2 3 − 6 9 − 33 2 − 3 11 | − 30 Thus, − 3 is not zero of the polynomial f ( x ) . Let 1 2 is zero of the polynomial. According to the synthetic division. 1 2 2 3 2 3 1 2 2 _ 2 4 4 | 5 Thus, 1 2 is not zero of the polynomial f ( x )

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Chapter 4.4, Problem 76E

To determine

To find:

The rational zeros of the polynomial f(x)=2x3+3x2+2x+3.

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Chapter 4.4, Problem 75E

Chapter 4.4, Problem 77E

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Chapter 4 Solutions

COLLEGE ALGEBRA-MML 18 WEEK ACCESS ONLY

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The rational zeros of the polynomial f ( x ) = 2 x 3 + 3 x 2 + 2 x + 3 .

To find: The rational zeros of the polynomial f(x)=2x3+3x2+2x+3.

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Chapter 4 Solutions

To find:

The rational zeros of the polynomial f(x)=2x3+3x2+2x+3.