Question

What is the greatest common factor of the expression: `32a^3b^2 + 36 a^2c- 16ab^3`?

Answer 1

The GCF is `4a`

Explanation:

`32, 36, and 16` are all divisible by 4 and nothing higher.

Each term has an `a`

`b and c` do not appear in all the terms, so they are not common.

The GCF is therefore `4a`

As a check , factor `4a` out and see if there is still a common factor.

`32a^3b^2 + 36 a^2c- 16ab^3`

`=4a(color(blue)(8a^2b^2 +9ac -4b^3))`

There is no common factor in `(color(blue)(8a^2b^2 +9ac -4b^3))`