The Remainder and Factor Theorems Worksheet with Answer Key

What's on the worksheet

1. Find each remainder without dividing:
   (x^3 - 4x^2 + 6) \div (x - 3)(2x^4 + x^3 - 5x) \div (x + 2)(x^{10} - 3x^7 + 2) \div (x + 1)(9x^3 - 3x^2 + 4x - 1) \div (3x - 1)
2. Decide without dividing whether x plus 3 is a factor, and give the remainder if not.
   x^3 + 27x^4 + 81x^5 + 3x^4 - x - 3
3. Use a point on the graph to factor a cubic completely and list its zeros.
4. Find k so a cubic leaves the same remainder for two divisors, and give that remainder.
5. Use a given zero to factor a cubic and find all three zeros.
6. Show three linear factors of a cubic and explain why they are all of it.