004 Sample Final A, Problem 8

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a) List all the possible rational zeros of the function
b) Find all the zeros, that is, solve

Foundations
If , what does the rational roots tell us are the possible roots of ?
Answer:
The rational roots tells us that the possible roots of are where is a divisor of .


Solution:

Step 1:
By the rational roots test, the possible roots of are .
Step 2:
Using synthetic division, we test 1 as a root of . We get a remainder of 0. So, we have that 1 is a root of .
By synthetic division, .
Step 3:
Using synthetic division on , we test 2 as a root of this function. We get a remainder of 0. So, we have that 2 is a root of .
By synthetic division, .
Step 4:
Thus, .
The zeros of are .
Final Answer:
The possible roots of are .
The zeros of are

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