Question

What is the fully factored from of 32a3+12a2

Answer 1

The fully factored form would be 4a^2(8a + 3)

In order to find this, we must find the greatest common factor. To do this, first find the term with the least number of a's. In this case, 12a^2 is the least with two. That means we can take out a^2.

Next we need to find the greatest constant we can pull out. To do so, use the factors of the smallest number (12) and find the largest that goes evenly into 32.

The factors are: 12, 6, 4, 3, 2, 1

12 does not go evenly into 32, nor does 6. However, 4 does. This means we can take 4 out and use it with the a^2 for the greatest common factor. This leaves us with:

4a^2(8a + 3)

Answer 2

32a^3 = 4a^2 x 8a

12a^2 = 4a^2 x 3

GCF = 4a^2

So

32a^3 + 12a^2 = 4a^2(8a + 3)

Hope it helps.