Grade 11 · Math · Algebra 2

11th grade Synthetic division, and the Remainder and Factor Theorems worksheet

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Synthetic division, and the Remainder and Factor Theorems

Grade 11 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Noah divides x³ + 5x² − 2x + 3 by x + 3 on a worksheet with synthetic division. Write the quotient, a comma, then the remainder. What are they?
In a notebook, Pia uses synthetic division for (2x³ − 3x² + 4x − 2) ÷ (x − 2). Write the quotient, a comma, then the remainder. What are they?
Ren divides x³ − 8x + 5 by x + 2 in pencil, the synthetic way. Write the quotient, a comma, then the remainder. What are they?
On a puzzle card, Tala works out (3x³ − 5x² + 8) ÷ (x − 2) by synthetic division. Write the quotient, a comma, then the remainder. What are they?
p(x) = x³ − 2x² + 3x + 5. Zee wants the remainder of p(x) ÷ (x + 2) without dividing, on a worksheet. What is the remainder?
p(x) = x³ + 2x² − 6x − 1. In pencil, Jun finds the remainder when p(x) is divided by x + 3. What is it?
On a puzzle card, Kira divides x³ − 4x² + x + 6 by x − 4 without doing the division. What is the remainder?
8.
p(x) = x³ − 6x² + 5x + 12. Luz tests the choices on a worksheet. Which one is a factor of p(x)?
- x + 3
- x − 2
- x + 2
- x − 3
9.
p(x) = x³ − 3x² − 13x + 15. In pencil, Noah checks each binomial. Which one is a factor of p(x)?
- x − 5
- x − 2
- x + 2
- x + 5
10.
On a puzzle card, p(x) = x³ + 3x² − 4x − 12. Pia needs a factor. Which one is it?
- x − 1
- x − 3
- x + 1
- x + 3

Synthetic division, and the Remainder and Factor Theorems. Every version has 10 questions, and the answer key prints on the second page.

I can divide by x − a with synthetic division.
I can find a remainder by working out p(a).
I can tell whether x − a is a factor, and find a missing number that makes it one.

Standard: A-APR.B.2

synthetic division: A short way to divide by x − a, using only the numbers.

the box number: The a in x − a: the x that makes the divisor 0.

Remainder Theorem: The remainder for x − a equals p(a).

Factor Theorem: x − a is a factor exactly when p(a) = 0.

Your child subtracted down the columns in synthetic division instead of adding. Try: do one column together, multiply then add.

Your child added down the columns without multiplying by the box number first. Try: say multiply, then add, for each column.

Your child left out a missing power instead of writing 0 for it. Try: write every power from the highest down, with 0 where one is missing.

What is the most common mistake with synthetic division, and the remainder and factor theorems?

Your child subtracted down the columns in synthetic division instead of adding. Try: do one column together, multiply then add.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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