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Synthetic division worksheets Grades 10–11

Divide a polynomial by x − c with synthetic division.

The front of the free synthetic division worksheet
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Free · Worked example · 18 problems · Answer key · US Letter

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How to do it

To divide by x − c, use c. Bring down the first number, multiply by c, add, and repeat. Write 0 for a missing term. The last number is the remainder.

(3x3−15x2+19x−3)÷(x−3)=3x2−6x+1(3x^{3} - 15x^{2} + 19x - 3) \div (x - 3) = 3x^{2} - 6x + 1
quotient 3x2−6x+1,remainder 0\text{quotient }3x^{2} - 6x + 1,\quad \text{remainder }0the bottom row, one degree lower

Example problems

  1. (2x3−5x2−17x+20)÷(x−4)=(2x^{3} - 5x^{2} - 17x + 20) \div (x - 4) =
  2. (2x2−3x−20)÷(x−4)=(2x^{2} - 3x - 20) \div (x - 4) =
  3. (x3+x2−26x−20)÷(x−5)=(x^{3} + x^{2} - 26x - 20) \div (x - 5) =
  4. (4x3−6x2−2x−9)÷(x−2)=(4x^{3} - 6x^{2} - 2x - 9) \div (x - 2) =

Quadratic and polynomial functions

  1. Vertex form of a quadratic
  2. Finding the vertex from standard form
  3. The discriminant
  4. Quadratic equations with complex roots
  5. Polynomial long division
  6. Synthetic division
  7. The remainder theorem
  8. The factor theorem
  9. The rational root theorem