Can 3x^2+2x-1 be factored?

3x² + 2x - 1 = 0
x² + 1/3x = 1/3 + (1/3)²
x² + 1/3x = 3/9 + 1/9
(x + 1/3)² = 4/9
x + 1/3 = ± 2/3

= x + 1/3 - 2/3, = x - 1/3, = 3x - 1
= x + 1/3 + 2/3, = x + 3/3, = x + 1

Answer: (3x - 1)(x + 1)

Proof:
= (3x - 1)(x + 1)
= 3x(x) + 3x(1) - 1(x) - 1(1)
= 3x² + 3x - x - 1
= 3x² + 2x - 1

I hope this is what you wanted.
3x^2 + 2x -1

=>3x^2 + 3x - x - 1

=>3x(x + 1) - 1(x + 1)

=>(x + 1)(3x - 1)

Factor 3x² + 2x - 1

( 3x - 1 )( x + 1 )

( 3 x - 1 ) ( x + 1 )

Definitely yes. To factor this find the factors of -3 so that their sum is 2. These are 3 and -1. So we write 2x as 3x - x.
3x^2+2x-1
= 3x^2 + 3x - x - 1
=3x( x + 1) - 1(x + 1)
= (3x - 1)(x + 1) (Answer)

Yes, it can be factored.

Factor completely.
3x^2 + 2x - 1
= 3x^2 + 3x - x - 1
= (3x^2 + 3x) - (x + 1)
= 3x(x + 1) - 1(x + 1)
= (x + 1)(3x - 1)

yes.

3x-1 * x+1

u can break it down but will still be left with (?) - 1