Algebra-2

To determine the possible rational roots of the polynomial function f(x) with a leading coefficient of 1 and a constant term of 6, we will apply the Rational Root Theorem.

 

Step 1: Identify the Factors

1.Constant Term: The constant term is 6.

2.Leading Coefficient: The leading coefficient is 1.

 

Factors of the Constant Term 6:

The factors of 6 are:

 

Factors of the Leading Coefficient 1:

The factors of 1 are:

 

Step 2: Possible Rational Roots

According to the Rational Root Theorem, the possible rational roots can be expressed as follows:

p is a factor of the constant term 6.

q is a factor of the leading coefficient 1.

 

Using these factors, the possible rational roots are:

From p = 1:

 

From p = -1:

 

From p = 2:

 

From p = -2:

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