Questions: Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x)=x^3-2x^2-13x+14 Choose the answer below that lists all possible rational zeros. A. -1,1,-2,2,-7,7,-14,14,-1/2, 1/2,-1/7, 1/7,-1/14, 1/14 B. -1,1,-14,14 C. -1,1,-2,2,-7,7,-14,14 D. -1,1,-1/2, 1/2,-1/7, 1/7,-1/14, 1/14

Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x)=x^3-2x^2-13x+14 Choose the answer below that lists all possible rational zeros. A. -1,1,-2,2,-7,7,-14,14,-1/2, 1/2,-1/7, 1/7,-1/14, 1/14 B. -1,1,-14,14 C. -1,1,-2,2,-7,7,-14,14 D. -1,1,-1/2, 1/2,-1/7, 1/7,-1/14, 1/14
Transcript text: Use the Rational Zero Theorem to list all possible rational zeros for the given function. \[ f(x)=x^{3}-2 x^{2}-13 x+14 \] Choose the answer below that lists all possible rational zeros. A. $-1,1,-2,2,-7,7,-14,14,-\frac{1}{2}, \frac{1}{2},-\frac{1}{7}, \frac{1}{7},-\frac{1}{14}, \frac{1}{14}$ B. $-1,1,-14,14$ C. $-1,1,-2,2,-7,7,-14,14$ D. $-1,1,-\frac{1}{2}, \frac{1}{2},-\frac{1}{7}, \frac{1}{7},-\frac{1}{14}, \frac{1}{14}$
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Solution

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Solution Steps

Step 1: Identify the leading coefficient and the constant term

The leading coefficient \(a_n\) is 1 and the constant term \(a_0\) is 14.

Step 2: List all positive and negative factors of the constant term \(a_0\)

The factors of the constant term \(a_0\) are: [1, 2, 7, 14, -1, -2, -7, -14]

Step 3: List all positive and negative factors of the leading coefficient \(a_n\)

The factors of the leading coefficient \(a_n\) are: [1, -1]

Step 4: Form all possible fractions

The possible rational zeros of the polynomial are: [-14, -7, -2, -1, 1, 2, 7, 14]

Final Answer:

The possible rational zeros of the polynomial, according to the Rational Zero Theorem, are: [-14, -7, -2, -1, 1, 2, 7, 14]

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