Divide polynomials by long division

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Ari divides 2x³ + 5x² − x + 7 by x + 3. The first quotient term is 2x². The next term is ▢x. What number goes in the box?

   -1
2. 2.

   Bo starts the long division (3x³ − 4x² + 2x + 9) ÷ (x − 3) and writes 3x² on top. The next term is ▢x. What number goes in the box?

   5
3. 3.

   On a puzzle card, Esme divides 2x³ + 7x − 3 by x − 4. The quotient starts 2x². The next term is ▢x. What number goes in the box?

   8
4. 4.

   Kira divides x³ + 6x² + 5x + 1 by x + 2 on a worksheet and gets the quotient x² + 4x − 3. What is the remainder?

   7
5. 5.

   Luz's long division of (2x³ − 7x² + 7x − 17) ÷ (x − 3) in a notebook gives the quotient 2x² − x + 4. What is the remainder?

   -5
6. 6.

   Noah divides 3x³ − 13x² − 11x + 11 by x − 5 in pencil. The quotient is 3x² + 2x − 1, and one piece is left over. What is the remainder?

   6
7. 7.

   Pia divides x³ + 2x² − 16x + 7 by x − 3 on a worksheet. The quotient is x² + 5x − 1 and the remainder is 4. Which shows the whole answer?

   • x² + 5x − 1 + 4/x
   • x² + 5x − 1 + 4/(x − 3)
   • x² + 5x − 1 + 4/(x² + 5x − 1)
   • x² + 5x − 1
8. 8.

   Ren's long division of (2x³ + x² − 5x − 1) ÷ (x + 2) in a notebook gives the quotient 2x² − 3x + 1, remainder -3. Which shows the whole answer?

   • 2x² − 3x + 1 − 3/x
   • 2x² − 3x + 1 − 3/(2x² − 3x + 1)
   • 2x² − 3x + 1 − 3/(x + 2)
   • 2x² − 3x + 1
9. 9.

   Tala divides x³ − 3x² + 2x − 19 by x − 4 from a math book: quotient x² + x + 6, remainder 5. Which way of writing the answer is right?

   • x² + x + 6 + 5/(x − 4)
   • x² + x + 6 + 5/(x² + x + 6)
   • x² + x + 6 + 5/x
   • x² + x + 6
10. 10.

    Zee finishes (3x³ + x² − 6x − 10) ÷ (x + 1) on a puzzle card with the quotient 3x² − 2x − 4 and remainder -6. Which shows the whole answer?

    • 3x² − 2x − 4 − 6/x
    • 3x² − 2x − 4
    • 3x² − 2x − 4 − 6/(3x² − 2x − 4)
    • 3x² − 2x − 4 − 6/(x + 1)