GP2-PAP-S5-HW5 Name:_________________________________________________Period: _______ Seat #______
Skill 5g: Using the Rational Root Theorem
1. List all of the possible zeros of the function 𝑓(𝑥) = 2𝑥 2 + 7𝑥 + 6 using the rational zero theorem. Then
find the zeros of 𝑓(𝑥) by factoring and confirm that they are in the list.
Factors of 𝑎0 :
Factors of 𝑎𝑛 :
List of Possible Zeros:
Actual Zeros:
2. List all of the possible zeros of the function 𝑓(𝑥) = 5𝑥 2 − 11𝑥 + 2 using the rational zero theorem. Then
find the zeros of 𝑓(𝑥) by factoring and confirm that they are in the list.
Factors of 𝑎0 :
Factors of 𝑎𝑛 :
List of Possible Zeros:
Actual Zeros:
3. List all of the possible zeros of the function 𝑓(𝑥) = 4𝑥 2 + 24𝑥 − 13 using the rational zero theorem. Then
find the zeros of 𝑓(𝑥) and confirm that they are in the list.
Factors of 𝑎0 :
Factors of 𝑎𝑛 :
List of Possible Zeros:
Actual Zeros:
4. List all of the possible zeros of the function 𝑓(𝑥) = 𝑥 3 + 9𝑥 2 + 20𝑥 + 12 using the rational zero theorem.
Use synthetic division and then factoring to find all zeros.
5. List all of the possible zeros of the function 𝑓(𝑥) = 2𝑥 3 + 3𝑥 2 − 2𝑥 − 3 using the rational zero theorem.
Use synthetic division and then factoring to find all zeros.
6. List all of the possible zeros of the function 𝑓(𝑥) = 𝑥 3 + 3𝑥 2 − 6𝑥 − 8 using the rational zero theorem.
Use synthetic division and then factoring to find all zeros.
7. List all of the possible rational zeros of the function 𝑓(𝑥) = 3𝑥 3 − 7𝑥 2 + 4 using the rational zero theorem.
Use synthetic division and then factoring to find all zeros. At each zero indicate if the graph crosses the x-axis,
or touches the x-axis.
Factors of 𝑎0 :
Factors of 𝑎𝑛 :
List of Possible Zeros:
Actual Zeros:
8. Factor out the GCF, then list all of the possible rational zeros of the function
𝑓(𝑥) = 𝑥 7 + 𝑥 6 − 2𝑥 5 − 2𝑥 4 + 𝑥 3 + 𝑥 2 using the rational zero theorem. Use synthetic division and then
factoring to find all zeros. At each zero indicate if the graph crosses the x-axis, or touches the x-axis.
Factors of 𝑎0 :
Factors of 𝑎𝑛 :
List of Possible Zeros:
Actual Zeros:
9. Factor out the GCF, then list all of the possible rational zeros of the function
𝑓(𝑥) = 8𝑥 5 + 8𝑥 3 − 160𝑥 using the rational zero theorem. Use synthetic division and then factoring to find
all zeros. At each zero indicate if the graph crosses the x-axis, or touches the x-axis.
Factors of 𝑎0 :
List of Possible Zeros:
Actual Zeros:
Factors of 𝑎𝑛 :