Math Problem Statement
Solution
I see that you've uploaded a worksheet titled 10.1 Adding and Subtracting Polynomials. Let me help you solve these problems step by step. Here's a breakdown:
1. (4x² - 2x + 8) + (x² + 3x - 2)
Combine like terms: Answer:
2. (4x² - 2x + 8) + (2x² + 2x - 5)
Combine like terms: Answer:
3. (5x² - x + 5) + (x² + x - 5)
Combine like terms: Answer:
4. (3x² - 3x + 4) + (x² + 3x - 6)
Combine like terms: Answer:
5. (2x² - 2x + 3) - (x² + 5x - 5)
Distribute the subtraction and combine like terms: Answer:
6. (2x² - 4x + 8) - (x² + 3x - 1)
Distribute the subtraction and combine like terms: Answer:
7. (6x² - 4x + 1) - (2x² + 6x - 1)
Distribute the subtraction and combine like terms: Answer:
8. (6x² - 2x + 2) - (5x² + 2x - 2)
Distribute the subtraction and combine like terms: Answer:
9. (7x² - 5x + 11) - (3x² + 2x - 11)
Distribute the subtraction and combine like terms: Answer:
10. (7x² - 8x + 10) - (2x² + x + 10)
Distribute the subtraction and combine like terms: Answer:
11. State the degree of the monomial .
The degree of a monomial is the highest power of the variable. Here, the degree is 4.
Answer:
12. Find the product of .
Distribute the : Answer:
Would you like further clarification or more detailed steps for any problem?
Here are five related questions to expand your understanding:
- How do you determine the degree of a polynomial?
- What is the process for combining like terms in a subtraction problem?
- How can distributing negative signs affect polynomial subtraction?
- How do you multiply a monomial with a polynomial?
- Can a polynomial have terms with fractional or negative exponents?
Tip: Always align like terms carefully while adding or subtracting polynomials to avoid mistakes.
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Math Problem Analysis
Mathematical Concepts
Polynomial addition
Polynomial subtraction
Combining like terms
Distributive property
Formulas
Combine like terms: ax^n + bx^n = (a + b)x^n
Distribute: a(b + c) = ab + ac
Theorems
Fundamental theorem of algebra for polynomial operations
Suitable Grade Level
Grade 8-10
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