Divide polynomials by long division

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Ari divides x³ + 4x² − 3x + 5 by x + 2 on a worksheet. Write the quotient, a comma, then the remainder. What are they?

   x^2 + 2x - 7, 19
2. 2.

   Bo works out (2x³ − 5x² + x − 4) ÷ (x − 2) in a notebook. Write the quotient, a comma, then the remainder. What are they?

   2x^2 - x - 1, -6
3. 3.

   Esme works out (x³ − 6x² + 2x + 7) ÷ (x − 4) in pencil. Write the quotient, a comma, then the remainder. What are they?

   x^2 - 2x - 6, -17
4. 4.

   Jun divides 3x³ + 7x² − 4x + 1 by x + 3 on a puzzle card. Write the quotient (powers like x^2), a comma, then the remainder. What are they?

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

   Kira divides x³ − 6x + 13 by x − 2 on a worksheet. One power is missing. Write the quotient, a comma, then the remainder. What are they?

   x^2 + 2x - 2, 9
6. 6.

   Luz works out (2x³ + 3x² − 4) ÷ (x + 2) in a notebook. Write the quotient, a comma, then the remainder. What are they?

   2x^2 - x + 2, -8
7. 7.

   Milo divides x³ + 4x² − 9 by x − 3 in pencil. Write the quotient, a comma, then the remainder. What are they?

   x^2 + 7x + 21, 54
8. 8.

   Ren checks four answers for (2x³ − x² + 6) ÷ (x + 2) in a math book. Which one is right?

   • 2x − 5 + 16/(x + 2)
   • 2x² − 5x + 10 − 14/(x + 2)
   • 2x² − 5x + 10
   • 2x² + 3x + 6 + 18/(x + 2)
9. 9.

   Tala works out (x³ + 3x − 2) ÷ (x + 4) in pencil. Which is the whole answer?

   • x² − 4x + 19 − 78/(x + 4)
   • x − 1 + 2/(x + 4)
   • x² − 4x + 19
   • x² + 4x + 19 + 74/(x + 4)
10. 10.

    Zee divides x³ − 2x² + 5 by x − 4 in a notebook, writing a 0 for the missing power. Which is the whole answer?

    • x² − 6x + 24 − 91/(x − 4)
    • x + 2 + 13/(x − 4)
    • x² + 2x + 8 + 37/(x − 4)
    • x² + 2x + 8