Question: Factor by grouping. 10x^3 - 12x^2 + 25x - 30

Solution

To factor the expression \(10x^3 - 12x^2 + 25x - 30\) by grouping, follow these steps: First, group the terms: \[ (10x^3 - 12x^2) + (25x - 30) \] Factor out the greatest common factor from each group. For the first group \(10x^3 - 12x^2\), the common factor is \(2x^2\): \[ 2x^2(5x - 6) \] For the second group \(25x - 30\), the common factor is \(5\): \[ 5(5x - 6) \] Now the expression looks like this: \[ 2x^2(5x - 6) + 5(5x - 6) \] Since both terms contain the common factor \((5x - 6)\), factor it out: \[ (5x - 6)(2x^2 + 5) \] So, the factored form of the expression is: \((5x - 6)(2x^2 + 5)\)