Question

How can we factories 3x^2+2x+1

Answer 1

I think your question is
3x^2+2x-1

To factories this
Splitting the middle term can be used

That is
2x can be written as 3x-1x

3x^2+(3x-1x)-1

We can write

(3x^2+3x)-x-1
=3x(x+1)-1(x+1)

=(x+1)(3x-1)
it is the factor of this


If your question is 3x^2+2x+1
Then factorisation is much more difficult