Math Problem Statement
Solution
The problem presented in the image asks for the division of the polynomial by and to include the remainder as a fraction if it doesn't divide evenly. Let's solve this using polynomial long division.
Step 1: Set up the division
We are dividing:
Step 2: Perform the division
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Divide the first term of the dividend by the first term of the divisor :
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Multiply by :
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Subtract from :
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Divide the new first term by :
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Multiply by :
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Subtract from :
Thus, the remainder is zero, and the quotient is:
Final Answer:
Would you like a breakdown of any of the steps or further details?
Here are some related questions for you to consider:
- How is synthetic division different from polynomial long division?
- What happens if the divisor has a higher degree than the dividend?
- Can you apply the remainder theorem to check the remainder?
- What is the impact of changing the divisor in this division problem?
- How would this problem change if the coefficients of and were different?
Tip: Always ensure the dividend is written in standard form with all missing terms (e.g., ) before starting long division.
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Math Problem Analysis
Mathematical Concepts
Polynomial Division
Algebraic Long Division
Formulas
Polynomial Long Division
Theorems
Division Algorithm for Polynomials
Suitable Grade Level
Grades 9-12
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