Questions: Factor the greatest common factor from the polynomial. 21 x^2+24 x Select the correct choice below and fill in any answer boxes A. 21 x^2+24 x= B. The polynomial is prime.

Solution Steps

To factor the greatest common factor (GCF) from the polynomial \(21x^2 + 24x\), we need to find the largest number and variable that can divide both terms.

1. Identify the GCF of the coefficients (21 and 24).
2. Identify the GCF of the variable parts (\(x^2\) and \(x\)).
3. Factor out the GCF from the polynomial.

To factor the polynomial \(21x^2 + 24x\), we first identify the greatest common factor (GCF) of the coefficients and the variable parts.

• The coefficients are 21 and 24. The GCF of 21 and 24 is 3.
• The variable parts are \(x^2\) and \(x\). The GCF of \(x^2\) and \(x\) is \(x\).

Next, we factor out the GCF from each term in the polynomial:

\[ 21x^2 + 24x = 3x(7x + 8) \]

Final Answer