Questions: Use the following function to answer parts a through c. f(x) = 7x^3 + 53x^2 + 29x + 7 a. List all possible rational zeros. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each)

Use the following function to answer parts a through c. f(x) = 7x^3 + 53x^2 + 29x + 7 a. List all possible rational zeros. (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type each)
Transcript text: Use the following function to answer parts a through c. \[ f(x)=7 x^{3}+53 x^{2}+29 x+7 \] a. List all possible rational zeros. $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type eac
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Solution

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Solution Steps

Step 1: List all factors of the constant term \(a_0\)

The factors of the constant term \(a_0 = 7\) are: -7, -1, 1, 7.

Step 2: List all factors of the leading coefficient \(a_n\)

The factors of the leading coefficient \(a_n = 7\) are: -7, -1, 1, 7.

Step 3: Form all possible fractions \(\frac{{p}}{{q}}\)

The possible rational zeros, simplified to their lowest terms, are: 1, 1/7, 7, -1/7, -7, -1.

Final Answer:

The possible rational zeros of the polynomial are: 1, 1/7, 7, -1/7, -7, -1.

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