# 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