Simplifying Polynomials Worksheet
Grade 12 Math worksheet focusing on simplifying polynomials through addition, subtraction, multiplication, and division.
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Topics
Simplifying Polynomials
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Read each question carefully and simplify the polynomials as instructed. Show all your work for full credit.
1. Simplify the following expression: (3x^3 + 2x^2 - 5x + 7) + (x^3 - 4x^2 + 2x - 3)
2. Simplify the following expression: (5y^4 - 2y^3 + 6y - 1) - (2y^4 + 3y^3 - 4y^2 + 5y)
3. Expand and simplify: (2x + 3)(x^2 - 4x + 5)
4. Expand and simplify: (x - 2)(x + 2)(x^2 + 4)
5. Divide (x^3 - 6x^2 + 11x - 6) by (x - 3).
6. The product of (x + 5) and (x - 5) is .
7. When you subtract (3x^2 - 2x + 1) from (5x^2 + x - 4), the result is .
8. The simplified form of (2x^2)^3 is .
9. The degree of the polynomial 4x^5 - 2x^7 + x - 1 is 5.
True
False
10. (x + y)^2 simplifies to x^2 + y^2.
True
False
11. Which of the following is equivalent to (x - 3)(x^2 + 3x + 9)?
x^3 - 27
x^3 + 27
x^3 - 6x^2 + 9x - 27
x^3 + 6x^2 - 9x + 27
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