Math Problem Statement
(2x*2-x+4)/(x+3)
Solution
To simplify the expression
we can attempt polynomial division to see if it can be broken down further.
Step 1: Polynomial Division
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Divide the leading term in the numerator, , by the leading term in the denominator, , which gives .
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Multiply by , resulting in .
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Subtract from , giving .
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Now, repeat the process with by dividing by , resulting in .
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Multiply by , resulting in .
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Subtract from , which leaves a remainder of .
Final Result
Thus, we have:
So, the simplified form of the expression is:
Would you like further details on any steps, or do you have any additional questions?
Here are some related questions that might interest you:
- How would this division change if the numerator were ?
- What are some common mistakes to avoid in polynomial division?
- How does polynomial division differ from synthetic division?
- Could this expression be further simplified if additional terms were added?
- How can you confirm the correctness of polynomial division?
Tip: Always double-check each step in polynomial division, especially when dealing with negative terms, to avoid errors in signs.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Division
Rational Expressions
Formulas
Polynomial Division Process
Theorems
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Suitable Grade Level
Grades 9-11
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