Combining Polynomials Worksheet
Grade 12 math worksheet on combining polynomials, including addition, subtraction, multiplication, and division.
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Combining Polynomials
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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)?
8x + 24
2x² + 8x + 8
x² + 8x + 24
8x + 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.