Math Problem Statement
- Determine the value of k so that x 2 is a factor of x3- 2kx2 +6x - 4.
Solution
To determine the value of such that is a factor of the polynomial , we need to use the Factor Theorem. According to the Factor Theorem, is a factor of the polynomial if and only if the polynomial evaluates to zero when .
Given the polynomial:
we need to find such that .
Step-by-Step Solution:
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Substitute into the polynomial:
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Simplify the expression:
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Set the expression equal to zero and solve for :
Conclusion:
The value of that makes a factor of is .
Would you like any details or have any questions? Here are some possible follow-up questions:
- How does the Factor Theorem work?
- Can you show another example using the Factor Theorem?
- What if the polynomial had more than one unknown coefficient?
- How do you perform polynomial long division?
- Could you demonstrate synthetic division for this problem?
Tip: When using the Factor Theorem, always verify your solution by substituting the found value back into the polynomial to ensure it evaluates to zero.
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Math Problem Analysis
Mathematical Concepts
Polynomials
Factor Theorem
Formulas
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Theorems
Factor Theorem
Suitable Grade Level
Grades 10-12
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