Polynomial Operations Worksheet

Polynomial Operations

Read each question carefully and show all your work. Simplify all expressions completely.

1. Simplify the following expression: (4x^3 - 2x^2 + 5x - 1) + (2x^3 + 3x^2 - 7x + 8)

2. Subtract (3x^4 + 5x^2 - x + 6) from (7x^4 - 2x^3 + 4x^2 + 9).

3. Multiply the polynomials: (2x - 3)(x^2 + 4x - 5)

4. Expand and simplify: (x + 2)^3

5. Divide using long division: (x^3 - 6x^2 + 11x - 6) ÷ (x - 2)

6. Use synthetic division to divide: (2x^4 - 5x^3 - 14x^2 + 5x + 6) ÷ (x + 2)

7. According to the Remainder Theorem, if a polynomial P(x) is divided by (x - c), then the remainder is P( ).

8. If (x - 3) is a factor of P(x) = x^3 - 4x^2 + ax + 6, then the value of 'a' must be  .

9. Which of the following is a factor of x^3 - 7x + 6?

10. The volume of a rectangular prism is given by V(x) = x^3 + 6x^2 + 11x + 6. If the length of the prism is (x + 1) and the width is (x + 2), find an expression for the height.