Synthetic division, and the Remainder and Factor Theorems

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   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?

   x^2 + 2x - 8, 27
2. 2.

   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?

   2x^2 + x + 6, 10
3. 3.

   Ren divides x³ − 8x + 5 by x + 2 in pencil, the synthetic way. Write the quotient, a comma, then the remainder. What are they?

   x^2 - 2x - 4, 13
4. 4.

   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?

   3x^2 + x + 2, 12
5. 5.

   In a notebook, Esme uses the Remainder Theorem on (2x³ + x² − 4x + 3) ÷ (x − 3). What is the remainder?

   54
6. 6.

   On a puzzle card, Kira divides x³ − 4x² + x + 6 by x − 4 without doing the division. What is the remainder?

   10
7. 7.

   p(x) = x³ − 6x² + 5x + 12. Luz tests the choices on a worksheet. Which one is a factor of p(x)?

   • x + 3
   • x − 3
   • x + 2
   • x − 2
8. 8.

   In a notebook, Milo uses the Factor Theorem on p(x) = x³ + x² − 10x + 8. Which is a factor?

   • x − 2
   • x − 3
   • x + 2
   • x + 3
9. 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. 10.

    On a puzzle card, p(x) = x³ + 3x² − 4x − 12. Pia needs a factor. Which one is it?

    • x − 3
    • x + 3
    • x − 1
    • x + 1