# Worksheet: Polynomial Long Division with Remainder

In this worksheet, we will practice finding the quotient and remainder when polynomials are divided, including the case when the divisor is irreducible.

Q1:

Use polynomial division to simplify .

• A
• B
• C
• D
• E

Q2:

Write in the form where the degree of is less than that of .

• A
• B
• C
• D
• E

Q3:

Find the remainder , and the quotient when is divided by .

• A,
• B,
• C,
• D,
• E,

Q4:

Write in the form .

• A
• B
• C
• D
• E

Q5:

Given that with a remainder of 19, rewrite in the form .

• A
• B
• C
• D
• E

Q6:

Find the remainder when is divided by .

Q7:

Find the remainder when is divided by .

Q8:

Write in the form of .

• A
• B
• C
• D
• E

Q9:

Find the remainder when is divided by .

Q10:

Write in the form .

• A
• B
• C
• D
• E

Q11:

Find the remainder when is divided by .

Q12:

Find the remainder and the quotient when is divided by .

• A,
• B,
• C,
• D,
• E,

Q13:

Find the remainder , and the quotient when is divided by .

• A,
• B,
• C,
• D,
• E,

Q14:

Write in the form .

• A
• B
• C
• D
• E

Q15:

Express the division in the form .

• A
• B
• C
• D
• E

Q16:

Use polynomial long division to find the quotient and the remainder for , where and .

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

Q17:

Write in the form .

• A
• B
• C
• D
• E

Q18:

Find the quotient and the remainder when is divided by .

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