Math Problem Statement
Solution
To solve this problem, we are given the cubic function and need to determine which of the given factors is a root.
The possible factors are:
We can use synthetic division or the Remainder Theorem, which states that if , then is a factor of the polynomial.
Let’s check each option by substituting the values into the function:
-
Testing :
, so is not a factor.
-
Testing :
, so is not a factor.
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Testing (from ):
, so is not a factor.
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Testing :
, so is a factor of the polynomial.
Conclusion:
The correct factor of the function is .
Would you like more details on this, or have any further questions? Here are some related questions to expand your understanding:
- How do you factor cubic polynomials in general?
- Can the synthetic division method be used to confirm factors of higher-degree polynomials?
- How does the Remainder Theorem help in determining factors?
- What would be the full factorization of ?
- How would the graph of this cubic polynomial look?
Tip: The Remainder Theorem is a quick way to check if a value is a root without fully factoring the polynomial.
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Math Problem Analysis
Mathematical Concepts
Algebra
Cubic Equations
Factorization
Formulas
f(x) = 2x^3 - x^2 - 13x - 6
Synthetic Division
Remainder Theorem
Theorems
Remainder Theorem
Suitable Grade Level
Grades 10-12
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