Questions: Factor out the greatest common factor from the following polynomial. 12 b^3 + 4 b^2 + 1

Transcript text: Factor out the greatest common factor from the following polynomial. \[ 12 b^{3}+4 b^{2}+1 \]

Solution

Solution Steps

To factor out the greatest common factor (GCF) from a polynomial, identify the GCF of the coefficients of the terms. Then, divide each term by the GCF and express the polynomial as a product of the GCF and the resulting polynomial.

Step 1: Identify the Polynomial

The given polynomial is

\[ 12b^3 + 4b^2 + 1. \]

Step 2: Determine the Greatest Common Factor (GCF)

The coefficients of the terms are \(12\), \(4\), and \(1\). The GCF of these coefficients is \(1\), as \(1\) is the only number that divides all three coefficients.

Step 3: Factor the Polynomial

Since the GCF is \(1\), factoring it out does not change the polynomial. Therefore, the polynomial remains

\[ 12b^3 + 4b^2 + 1. \]