Tamara says she used the GCF to factor the expression 21x + 56xy as 7(3x + 8xy). Is she correct? Explain. Yes; 7 is the GCF. No; 7xy is the GCF. No; 14 is the GCF. No; 7x is the GCF.

The coefficients are 21 and 56.
Factors of 21: 1, 3, 7, 21
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
The greatest common factor of 21 and 56 is 7.

The variable terms are $x$ and $xy$.
The common variable is $x$. The lowest power of $x$ is $x^1$.
The variable $y$ is not common to both terms.
The GCF of the variable terms is $x$.

The GCF of $21x$ and $56xy$ is the product of the GCF of the coefficients and the GCF of the variables:
$\text{GCF} = 7 \times x = 7x$.

Tamara used 7 as the common factor. While 7 is a common factor, it is not the greatest common factor. The GCF is $7x$.
If the expression were factored using the GCF, it would be:
$21x + 56xy = 7x(3) + 7x(8y) = 7x(3 + 8y)$.

Therefore, Tamara is incorrect because $7x$ is the GCF, not 7.

The final answer is $\text{No; 7x is the GCF.}$