Lesson Worksheet: Rational Zeros Theorem Mathematics • 10th Grade
In this worksheet, we will practice using the rational zeros theorem to list all possible rational zeros in a given polynomial function.
Q1:
Using the rational zeros theorem, you can list all the possible rational zeros of the function .
What is the smallest possible rational zero?
What are the two possible rational zeros closest to zero?
- A,
- B,
- C, 1
- D,
- E,
What are the rational zeros, if any, of ?
- A, , 3
- B2, ,
- C, , 1
- D2, ,
Q2:
The rational zeros theorem can be used to generate a list of all possible rational zeros of a polynomial which we can then check one by one. How many possible rational zeros does the rational zeros theorem give us for the function ?
Q3:
The rational zeros theorem can be used to generate a list of all possible rational zeros of a polynomial which we can then check one by one. How many possible rational zeros does the rational zeros theorem give us for the function ?
Q4:
The cross section of a skate banister, shown in the diagram, can be modeled with the polynomial function , where is the height above the ground and is the horizontal distance from point .
Using the rational zeros theorem or otherwise, determine the horizontal distance between point and point , given that point is m above the ground.
- A3 m
- B m
- C m
- D1 m
- E m
Q5:
If , is a zero of , and , , and are integer numbers, which of the following can be the value of ?
- A
- B
- C
- D
- E
Q6:
True or False: If and is a zero of , then can be found using the rational zeros theorem.
- AFalse
- BTrue
Q7:
Consider the rational zeros theorem for the function .
Determine all factors of the constant term of .
- A and
- B, , , and
- C, , , and
- D and
- E and
Determine all factors of the leading coefficient of .
- A, , , and
- B and
- C and
- D and
- E, , , and
Determine all possible rational zeros of .
- A, , , , , and
- B, , , and
- C, , , , , , , and
- D, , , , , and
- E, , , , , and
Determine the rational zeros of .
- A, , and
- B, 3, and
- C1, , and
- D1, 3, and
- E1, , and
Q8:
True or False: If is a polynomial with integer coefficients and 2 is a zero of , then this zero can be found using the rational zeros theroem.
- AFalse
- BTrue
Q9:
Use the rational zeros theorem to find the rational zeros of .
- A, 2, , and
- B, 2, , and
- C1, , , and
- D1, , , and
- E1, , , and
Q10:
Using the rational zeros theorem, list all the possible rational zeros of the function .
- A
- B
- C
- D
- E