Grade 11 · Math · Algebra 2

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Synthetic division, and the Remainder and Factor Theorems

Grade 11 Math Worksheet - Building Confidence

NameDate

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

Luz divides x³ − 4x² + 2x + 8 by x − 3 on a worksheet, using synthetic division with 3 in the box. What is the remainder?
Noah divides x³ − 5x + 4 by x − 3 in pencil. The synthetic box holds 3. What is the remainder?
Pia uses synthetic division on a puzzle card: (2x³ − 5x² + 7) ÷ (x + 3), box -3. What is the remainder?
Ren divides x³ + 3x² − 4x + 7 by x − 2 on a worksheet. The synthetic bottom row is 1, 5, 6, 19. Type powers like x^2. What is the quotient?
Zee divides x³ − 2x² − 5x + 9 by x − 3 in pencil and gets the bottom row 1, 1, -2, 3. What is the quotient?
On a puzzle card, synthetic division of (3x³ + 4x² − 2x + 1) ÷ (x + 2) gives Esme the row 3, -2, 2, -3. What is the quotient?
p(x) = x³ − 2x² + 4x + 3. Jun wants the remainder of p(x) ÷ (x − 3) on a worksheet. The remainder is p(3). What is p(3)?
p(x) = 2x³ + 3x² − 5x + 1. In a notebook, Kira finds the remainder for x + 2 as p(-2). What is p(-2)?
p(x) = x³ + 4x² − 3x + 2. In pencil, Luz gets the remainder for x − 2 from p(2). What is p(2)?
On a puzzle card, p(x) = x³ − 3x² + 5x − 4. Milo knows the remainder for x + 3 is p(-3). What is p(-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.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records