Combining Polynomials Worksheet

Combining Polynomials

Read each question carefully and perform the indicated operations on the polynomials. Simplify your answers completely.

1. Add the following polynomials: (3x³ - 2x² + 5x - 8) + (x³ + 4x² - 2x - 1)

2. Subtract the second polynomial from the first: (7y⁴ + 3y² - 10) - (2y⁴ - y³ + 5y² - 6y + 3)

3. Multiply the following binomials: (2x + 3)(x - 5)

4. Expand the following expression: (3m - 2)(m² + 4m - 1)

5. When dividing x² - 5x + 6 by x - 2, the quotient is   and the remainder is  .

6. Using synthetic division, if (x³ + 4x² - x - 10) is divided by (x + 2), the quotient is  .

7. Which of the following is the simplified form of (x + 4)² - (x² - 8)?

8. The length of a rectangle is represented by (2x + 5) and its width by (x - 3). Find the perimeter of the rectangle in terms of x.

9. If the area of a rectangle is given by the polynomial (x² + 7x + 12) and its length is (x + 3), find the width of the rectangle.