Help with factoring

Question

Original Polynomial: 6a^3b + 36a^2b +48a^4b

Factored Polynomial: 3ab(2a^2 + 12a + 16a^3)

Explain why the factored polynomial above is not factored completely. 

Answer 1

Because 2a^2 + 12a + 16a^3 can be factored more.

You can factor "2a" 2a^2 + 12a + 16a^3 = 2a (a+6+8a²)

6a^3b + 36a^2b +48a^4b =3ab⋅ 2a (a+6+8a²) = 6a² b(a+6+8a²)

You'd better factor out the greatest common factor in the first place. It's not 3ab, but 6a²b so that you can get the answer at a time.

6a^3b + 36a^2b +48a^4b = 6a² b(a+6+8a²)