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 - Challenge Me

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

On a worksheet, x − 2 is a factor of x³ − 3x² + cx − 8. Ren needs the number c. What is c?
In a notebook, Tala learns that x + 2 is a factor of x³ + cx² − 5x + 10. What is c?
Zee knows x + 3 divides x³ − x² + cx + 18 with no remainder, and works in pencil. What is c?
On a puzzle card, x³ + 4x² + cx − 14 has the factor x + 2. Esme wants c. What is c?
On a worksheet, x³ + cx² + x + 7 divided by x + 1 leaves the remainder 3. Jun needs c. What is c?
In a notebook, Kira finds that (x³ + 2x² + cx − 14) ÷ (x − 2) has remainder -4. What is c?
On a puzzle card, (2x³ + x² + cx + 10) ÷ (x + 1) leaves 4. Milo wants c. What is c?
On a worksheet, x − 3 is a factor of x³ − x² − 11x + 15. Noah divides it out. Type powers like x^2. What is the other factor?
In a notebook, Pia uses synthetic division to take the factor x − 2 out of 2x³ + 3x² − 11x − 6. What is the other factor?
On a puzzle card, 3x³ − 2x² − 7x − 2 has the factor x + 1. Tala wants the quadratic factor. What is it?

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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