Question
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Use the rational zeros theorem to list all possible zeros of the function .
Enter the possible zeros separated by commas. You do not need to factor the polynomial.

Ask by Bob Campbell. in the United States
Jan 31,2025

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Tutor-Verified Answer

Answer

The possible rational zeros are: -3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3.

Solution

The possible rational zeros of the function can be determined using the Rational Zeros Theorem.
According to the theorem, any possible rational zero is of the form , where:
  • is a factor of the constant term (which is 3).
  • is a factor of the leading coefficient (which is 5).
Factors of 3 (constant term): ±1, ±3
Factors of 5 (leading coefficient): ±1, ±5
Thus, the possible rational zeros are:
Listing them out:
Answer:
-3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

To apply the rational zeros theorem, we first need to identify the factors of the constant term (3) and the leading coefficient (5). The factors of 3 are ±1, ±3, and the factors of 5 are ±1, ±5.
Now, we can form all the possible combinations of these factors in the form of , where is a factor of 3 and is a factor of 5. This results in the possible rational zeros:
±1, ±3, ± , ±
So, the complete list of possible rational zeros is:
1, -1, 3, -3, , - , , -

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