How would you rewrite the exspression 30a^3+40a^5 by factoring out the GCF

Answer 1

To factor the expression \(30a^3 + 40a^5\) by finding the greatest common factor (GCF), we first identify the GCF of the coefficients and the variable part.

1. Coefficients: The coefficients are 30 and 40. The GCF of 30 and 40 is 10.

2. Variable part: The variable part consists of \(a^3\) and \(a^5\). The GCF is \(a^3\) since it's the lowest power of \(a\).

Now, we can factor out the GCF:

\[ 30a^3 + 40a^5 = 10a^3(3 + 4a^2) \]

Therefore, the expression \(30a^3 + 40a^5\) factored by pulling out the GCF is:

\[ 10a^3(3 + 4a^2) \]