How would you rewrite the expression 6a2+12a5

Question

by factoring out the GCF?

Answer 1

To rewrite the expression \( 6a^2 + 12a^5 \) by factoring out the greatest common factor (GCF), we first need to determine the GCF of the coefficients and the variables.

1. Coefficients: The GCF of the coefficients 6 and 12 is 6.
2. Variables: The GCF of \( a^2 \) and \( a^5 \) is \( a^2 \), since the lowest power of \( a \) present in the terms is \( a^2 \).

Now, we can factor out the GCF, which is \( 6a^2 \):

\[ 6a^2 + 12a^5 = 6a^2(1 + 2a^3) \]

Thus, the expression \( 6a^2 + 12a^5 \) factored out by the GCF is:

\[ 6a^2(1 + 2a^3) \]