Question

factor the polynomial

6x^3+21x^2+15x

Answer 1

Take 3x common :)

Answer 2

Is there anything the three terms have in common that you could factor out first?

Answer 3

3x

Answer 4

If you factored out 3x, you'd get 3x (2x^2 +7x + 5).
Then you break it open/unfoil it, which requires a little educated guessing so that you can make it 3x(something)(something else).
First, you look at the 2x^2 part. What times what gives you 2x^2? A good answer would be 2x and x, nothing else works. So we have 3x(2x something)(x something).
Then we look at the 5. What multiplied together gives 5? 1 and 5, nothing else works. So, the answer could be 3x(2x+1)(x+5) or 3x(2x+5)(x+1). Check which by foiling them.
The answer is 3x(2x+5)(x+1), since it gives 3x(2x^2 +2x +5x +5), which is what you had after factoring out 3x.