Factor \( 3 x^{2}-11 x+6 \) \( (3 x-3)(x+2) \) \( (3 x+1)(x+1) \) \( (3 x-2)(x-3) \)

To factor the quadratic expression \( 3x^2 - 11x + 6 \), we look for two numbers that multiply to \( 3 \times 6 = 18 \) and add to \(-11\). The pair that fits this criteria is \(-9\) and \(-2\). We can rewrite the middle term: \[ 3x^2 - 9x - 2x + 6 \] Now, factor by grouping: \[ 3x(x - 3) - 2(x - 3) \] Which factors to: \[ (3x - 2)(x - 3) \] Hence, the correct factorization is \( (3x - 2)(x - 3) \). As for the incorrect options provided: - \( (3x - 3)(x + 2) \) does not yield the correct middle term when expanded. - \( (3x + 1)(x + 1) \) also fails to match the original equation upon distribution.