Divide polynomials by long division

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

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

   2x^2 - x + 4, -9
2. 2.

   Esme divides 4x³ + 2x² − 18x + 11 by 2x + 5 in pencil; the first step is 4x³ ÷ 2x = 2x². Write the quotient, a comma, then the remainder. What are they?

   2x^2 - 4x + 1, 6
3. 3.

   Jun works out (8x³ − 10x² − 9x + 14) ÷ (2x − 3) on a math club puzzle card. Write the quotient, a comma, then the remainder. What are they?

   4x^2 + x - 3, 5
4. 4.

   Kira divides x⁴ − 5x² + 2x − 5 by x + 2 on a worksheet. Write the quotient (powers like x^3), a comma, then the remainder. What are they?

   x^3 - 2x^2 - x + 4, -13
5. 5.

   Luz works out (x⁴ + 2x³ − 6x + 1) ÷ (x + 3) in a notebook. Write the quotient, a comma, then the remainder. What are they?

   x^3 - x^2 + 3x - 15, 46
6. 6.

   Milo divides x⁴ − 6x² + x + 7 by x − 2 in pencil. Write the quotient, a comma, then the remainder. What are they?

   x^3 + 2x^2 - 2x - 3, 1
7. 7.

   Pia divided a polynomial by x − 3 on a worksheet. The quotient was x² + 2x − 1 and the remainder 4. Type powers like x^2. What was the polynomial?

   x^3 - x^2 - 7x + 7
8. 8.

   In a notebook, Ren divides a polynomial by x + 2. The quotient is 2x² − x + 3, remainder -5. What was the polynomial?

   2x^3 + 3x^2 + x + 1
9. 9.

   Tala divided a polynomial by x + 5 on a puzzle card and got x² − 4x, remainder 3. What was the polynomial?

   x^3 + x^2 - 20x + 3
10. 10.

    Zee's division by x − 1, in pencil, gave the quotient 3x² + x − 2 and the remainder 6. What polynomial was divided?

    3x^3 - 2x^2 - 3x + 8