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A polynomial function with integer coefficients has a leading coefficient of and a constant term of . According to the Rational Root Theorem, which of the following are possible roots of ?Multi-select Choices:(A) (B) (C) (D)
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Q. A polynomial function with integer coefficients has a leading coefficient of and a constant term of . According to the Rational Root Theorem, which of the following are possible roots of ?Multi-select Choices:(A) (B) (C) (D)
- Rational Root Theorem: The Rational Root Theorem states that any rational root, in the form of (where and are integers and ), of a polynomial equation with integer coefficients is such that is a factor of the constant term and is a factor of the leading coefficient.
- Leading Coefficient: Since the leading coefficient is , any rational root will have a denominator of , meaning it must be an integer.
- Factors of Constant Term: List the factors of the constant term : , , , .
- Checking Potential Roots: Check each option against the list of factors:(A) is a factor of , so it could be a root.(B) is not an integer, so it cannot be a root.(C) is a factor of , so it could be a root.(D) is a factor of , so it could be a root.
