Algebra-2

To determine the possible rational roots of the polynomial function f(x) with a leading coefficient of 3 and a constant term of -9, we can apply the Rational Root Theorem.

Step 1: Identify the Factors

1.Constant Term: -9

2.Leading Coefficient: 3

 

Factors of the Constant Term -9:

The factors of -9 are:

 

Factors of the Leading Coefficient 3:

The factors of 3 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 -9.

q is a factor of the leading coefficient 3.

 

Using these factors, the possible rational roots are:

From p = 1:

 

From p = -1:

 

From p = 3:

 

From p = -3:

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