AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
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)
Full solution
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)
- Understand Rational Root Theorem: The Rational Root Theorem states that any rational root, expressed in its simplest form , must have as a factor of the constant term and as a factor of the leading coefficient.
- Factor Constant Term: List the factors of the constant term : , .
- Factor Leading Coefficient: List the factors of the leading coefficient : , .
- Generate Possible Roots: Generate the possible rational roots by combining the factors of the constant term with the factors of the leading coefficient: , , , .
- Simplify Roots List: Simplify the list of possible rational roots: , , , .
- Compare with Given Choices: Compare the simplified list of possible roots with the given choices:(A) is not a possible root because is not a factor of the leading coefficient.(B) is not a possible root because is not a factor of the constant term.(C) is a possible root because is a factor of the constant term and is a factor of the leading coefficient.(D) is not a possible root because is not a factor of the leading coefficient.
