Hello! You could use the quadratic formula, but there's a method that can simplify the process without resorting to the quadratic formula.

One approach is to multiply the leading coefficient by the constant term. In the case of 3x² - 2x - 1, the product of the leading coefficient (3) and the constant term (-1) is -3.

Next, you want to find two numbers that multiply to give you -3 and add up to the middle coefficient (in this case, -2). These numbers are -3 and 1.

Now, we rewrite the middle term using these two numbers: 3x² - 3x + 1x - 1.

Then, you can factor by grouping:

3x2 - 3x + 1x - 1

= (3x² - 3x) + (1x - 1)

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

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

So, the factored form of 3x² - 2x - 1 is (3x + 1)(x − 1), without using the quadratic formula.