10a^2 + 25a - 15

factor out the GCF.

The GCF is 5

So
10a^2 + 25a - 15
=5(2a^2+5a-3)
(if necessary)
=5(2a-1)(a+3)

To factor out the greatest common factor (GCF) of the expression 10a^2 + 25a - 15, we need to identify the common factors that the terms share. In this case, the GCF is 5 because it is the largest common factor of all three terms:

10a^2 = 2 * 5 * a * a
25a = 5 * 5 * a
-15 = -1 * 5 * 3

Now, we can factor out the GCF from each term:

10a^2 + 25a - 15 = (2 * 5 * a * a) + (5 * 5 * a) + (-1 * 5 * 3)
= 5(2a^2) + 5(5a) - 5(3)

We can now factor out the common factor 5 from each term:

10a^2 + 25a - 15 = 5(2a^2 + 5a - 3)

Therefore, after factoring out the GCF, the expression becomes 5(2a^2 + 5a - 3).