Math Problem Statement
Solution
To determine which of the function operations are correct, let’s evaluate the provided functions step by step.
Given Functions:
Option A:
We divide by :
We perform polynomial long division:
- Divide by , which gives .
- Multiply back: .
- Subtract: .
- Divide by , which gives .
- Multiply back: .
- Subtract: .
Thus,
Option A is correct.
Option B:
We subtract from :
Simplify:
Thus, .
Option B is incorrect.
Option C:
We multiply and :
Use the distributive property:
Simplify:
Combine like terms:
Option C is correct.
Option D:
We subtract from :
Simplify:
Thus, .
Option D is incorrect.
Option E:
We add to :
Simplify:
Combine like terms:
Option E is correct.
Final Answers:
The correct options are:
A, C, and E.
Do you need further clarifications or step-by-step solutions for any part? Let me know!
5 Related Questions:
- How do you perform polynomial long division step-by-step?
- How do you combine like terms when adding or subtracting polynomials?
- How do you distribute terms when multiplying binomials?
- What is the difference between function addition and subtraction?
- How can you verify the result of polynomial division?
Tip:
Always simplify expressions and combine like terms carefully to avoid errors in polynomial operations.
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Math Problem Analysis
Mathematical Concepts
Polynomial Operations
Function Addition
Function Subtraction
Polynomial Multiplication
Polynomial Division
Formulas
Polynomial Division: (f ÷ g)(x)
Polynomial Addition/Subtraction: f(x) ± g(x)
Polynomial Multiplication: g(x) ⋅ h(x)
Theorems
Distributive Property
Polynomial Division Theorem
Suitable Grade Level
Grades 9-11
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