Polynomial Simplification Worksheet
Grade 12 Math worksheet focusing on simplifying polynomial expressions through addition, subtraction, multiplication, and division.
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Topics
Polynomial Simplification
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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?
2x + 5
10x + 5
10x
2x² + 2x + 5
8. Simplify the expression: (x + 1)(x - 1)(x² + 1) - (x⁴ - 1)