factor: 6x^2-13x+6

(3x-2)(2x-3)

To factor the expression 6x^2 - 13x + 6, we need to find two binomial factors whose product equals the given expression.

First, we look for two numbers that can multiply to give 6 * 6 = 36 (product of the first and last coefficients) and simultaneously add up to -13 (the middle coefficient). By examining the options, we find that -4 and -9 fit these criteria.

Now, we rewrite the expression using these numbers:

6x^2 - 13x + 6 = 6x^2 - 4x - 9x + 6

Next, we group the terms in pairs:

(6x^2 - 4x) + (-9x + 6)

From each group, we can factor out the greatest common factor:

2x(3x - 2) - 3(3x - 2)

Notice that we have a common binomial factor, 3x - 2. We can factor it out:

(2x - 3)(3x - 2)

Therefore, the factored form of 6x^2 - 13x + 6 is (2x - 3)(3x - 2).