Polynomial Simplification Worksheet

Polynomial Simplification

Read each question carefully and simplify the polynomial expressions as indicated. Show all your work for full credit.

1. Simplify the following expression: (3x³ - 2x² + 5x - 1) + (x³ + 4x² - 2x + 7)

2. Subtract the second polynomial from the first: (7y⁴ + 3y² - 2y + 8) - (2y⁴ - y³ + 5y² - 6)

3. Expand and simplify: (2x + 3)(x² - 4x + 5)

4. Find the product of the two polynomials: (x - 2y)(x² + 2xy + 4y²)

5. When dividing x³ - 6x² + 11x - 6 by x - 1, the quotient is   and the remainder is  .

6. Using synthetic division, if (x + 2) is a factor of x³ + 5x² + 7x + 2, then the other factor is  .

7. Which of the following is the simplified form of (x + 3)² - (x - 2)²?

8. Simplify the expression: (x + 1)(x - 1)(x² + 1) - (x⁴ - 1)