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Chapter 2: Problem 9

Use the Rational Zero Theorem to list possible rational zeros for each polynomial function. $$P(x)=2 x^{3}+x^{2}-25 x+12$$

Short Answer

Expert verified
The possible rational zeros of the polynomial \(P(x)=2x^{3}+x^{2}-25x+12\) are 卤1, 卤2, 卤3, 卤4, 卤6, 卤12, 卤1/2, 卤3/2.

Step by step solution

01

Identifying the Constant and Leading Coefficients

The constant term is the integer without a variable, which here is 12. The leading coefficient is the coefficient in front of the term with the highest power of x, which is 2 in our case.
02

Listing the Factors

The factors of 12 are: 卤1, 卤2, 卤3, 卤4, 卤6, 卤12. The factors of 2 are: 卤1, 卤2.
03

Form Possible Rational Zeros

Now, form the possible rational zeros by taking each factor of the constant term and dividing it by each factor of the leading coefficient. Here the possible rational solutions include 卤1, 卤2, 卤3, 卤4, 卤6, 卤12, 卤1/2, 卤3/2.

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