Algebra-2

To determine the possible rational roots of the polynomial function f(x) with a leading coefficient of 2 and a constant term of 5, we can use the Rational Root Theorem. According to this theorem, the possible rational roots can be expressed as follows:

 

p (the numerator) is a factor of the constant term 5.

q (the denominator) is a factor of the leading coefficient 2.

 

Step 1: Find Factors of the Constant Term 5

The factors of 5 are:

 

Step 2: Find Factors of the Leading Coefficient 2

The factors of 2 are:

 

Step 3: Possible Rational Roots

Using the Rational Root Theorem, we can list the possible rational roots  where p is a factor of 5 and q is a factor of 2:

From p = 1:

 

From p = -1:

 

From p = 5: