# Worksheet: Zeros of Polynomial Functions

In this worksheet, we will practice finding the set of zeros of a quadratic, cubic, or higher-degree polynomial function.

Q1:

Find, by factoring, the zeros of the function .

• A
• B
• C
• D
• E

Q2:

What are the zeros of the function ?

• A and
• B and
• C and
• D and
• E and

Q3:

Find, by factoring, the zeros of the function .

• A
• B
• C
• D
• E

Q4:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q5:

If the set of zeros of the function is , find the value of .

Q6:

Find, by factoring, the zeros of the function .

• A
• B
• C
• D
• E

Q7:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q8:

Find the set of zeros of the function .

• A
• B
• C
• D

Q9:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q10:

, , and . Find the other roots of and the value of .

• A, ,
• B, ,
• C, ,
• D,
• E, ,

Q11:

Find all the zeros of and state their multiplicities.

• A with multiplicity 1, with multiplicity 1, with multiplicity 1
• B with multiplicity 2, with multiplicity 2
• C with multiplicity 1, with multiplicity 1
• D with multiplicity 1, with multiplicity 2

Q12:

Which of the following functions have the same set of zeros?

• A and
• B and
• C and
• D and
• E and

Q13:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q14:

The function and the function have the same set of zeros. Find and the set of zeros.

• A,
• B,
• C,
• D,
• E,

Q15:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q16:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q17:

Given the function , determine the vertical and horizontal intercepts.

• AVertical intercept: or 2; horizontal intercept:
• BVertical intercept: , or 4; horizontal intercept:
• CVertical intercept: ; horizontal intercept: or 2
• DVertical intercept: ; horizontal intercept: , or 4

Q18:

What is the set of zeros of the function ?

• A
• B
• C
• D
• E

Q19:

Find the set of zeros of the function .

• A
• B
• C
• D
• E

Q20:

Consider the function .

Given that one zero of is , find all zeros of using synthetic division.

• A
• B
• C
• D
• E

Write the linear factorization of .

• A
• B
• C
• D
• E

Q21:

Consider .

Given that one zero of multiplicity 2 of is , find all zeros of using synthetic division.

• A
• B
• C
• D

Write the linear factorization of .

• A
• B
• C
• D

Q22:

Consider the function .

Given that one zero of is , find all zeros of using synthetic division.

• A, , ,
• B, , ,
• C, , ,
• D, , ,
• E, , ,

Write the linear factorization of .

• A
• B
• C
• D
• E

Q23:

Consider .

Given that one zero of is , find all zeros of using synthetic division.

• A, , , 2
• B, , 2
• C, , ,
• D, , ,

Write the linear factorization of .

• A
• B
• C
• D

Q24:

If is an integral domain and is a polynomial with coefficients in , then which of the following is true of ?

• A is a constant polynomial.
• B is irreducible.
• C must have a unique factorization.
• D is either irreducible or factorable.

Q25:

Given that and , find the other roots of .

• A,
• B,
• C,
• D,
• E,