Factor by grouping. \[ 2 x^{3}-3 x^{2}-4 x+6 \]

To factor the expression \( 2x^3 - 3x^2 - 4x + 6 \) by grouping, we start by grouping the terms in pairs: 1. Group the first two terms and the last two terms: \( (2x^3 - 3x^2) + (-4x + 6) \). 2. Factor out the common factors in each group: - From \( 2x^3 - 3x^2 \), we can factor out \( x^2 \), giving us \( x^2(2x - 3) \). - From \( -4x + 6 \), we can factor out \( -2 \), giving us \( -2(2x - 3) \). Now the expression looks like this: \[ x^2(2x - 3) - 2(2x - 3) \] 3. Notice that both terms contain the common factor \( (2x - 3) \): \[ (2x - 3)(x^2 - 2) \] So, the fully factored form of the expression \( 2x^3 - 3x^2 - 4x + 6 \) is: \[ (2x - 3)(x^2 - 2) \] This gives us our final factored result!