Math Problem Statement
Is
Solution
To determine if is a factor of , we can perform polynomial division or use synthetic division.
Step 1: Set up the division
We will divide by .
Step 2: Perform the division
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Divide the leading term of the dividend by the leading term of the divisor : So, the first term of the quotient is .
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Multiply the entire divisor by and subtract it from the original polynomial: Subtract this from the original polynomial:
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Repeat the process with the new polynomial : Divide the leading term by the leading term : So, the next term in the quotient is .
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Multiply the entire divisor by and subtract: Subtract this from :
Step 3: Conclusion
Since the remainder is , which is not zero, is not a factor of .
Would you like to see a detailed explanation or have any questions about this process?
Here are five related questions for further exploration:
- How can you use the Remainder Theorem to check if a polynomial is a factor?
- What is synthetic division, and how does it differ from polynomial division?
- How would you factor completely?
- What is the relationship between roots of a polynomial and its factors?
- Can divide another polynomial, like ?
Tip: Always verify your results by multiplying the quotient and the divisor to ensure the division was performed correctly.
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Math Problem Analysis
Mathematical Concepts
Polynomial division
Synthetic division
Formulas
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Theorems
Remainder Theorem
Suitable Grade Level
Advanced High School
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