Question
The following function is given.
a. List all rational zeros that are possible according to the Rational Zero Theorem.
(Use a comma to separate answers as needed.)
b. Use synthetic division to test several possible rational zeros in order to identify one actual zero.
One rational zero of the given function is
(Simplify your answer.)
a. List all rational zeros that are possible according to the Rational Zero Theorem.
(Use a comma to separate answers as needed.)
b. Use synthetic division to test several possible rational zeros in order to identify one actual zero.
One rational zero of the given function is
(Simplify your answer.)
Ask by Schwartz Ward. in the United States
Nov 09,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
One rational zero of the given function is 3.
Solution

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The Deep Dive
To identify the possible rational zeros for the function
, we apply the Rational Zero Theorem, which states that any potential rational zero, p/q, is a factor of the constant term (75) over a factor of the leading coefficient (1). Hence, the possible rational zeros are
.
Now, let’s test one of these values using synthetic division. Choosing
:
3 | 1 -3 -25 75
| 3 0 -75
---------------------
1 0 -25 0
The remainder is 0, confirming that
is an actual zero of the function
.