Question: Factor by grouping. 5x^3 + 4x^2 + 35x + 28

Solution

To factor the polynomial \(5x^3 + 4x^2 + 35x + 28\) by grouping, follow these steps: First, group the terms: \[ (5x^3 + 4x^2) + (35x + 28) \] Factor out the greatest common factor from each group. From the first group \(5x^3 + 4x^2\), factor out \(x^2\): \[ x^2(5x + 4) \] From the second group \(35x + 28\), factor out \(7\): \[ 7(5x + 4) \] Now, the expression becomes: \[ x^2(5x + 4) + 7(5x + 4) \] Notice that \((5x + 4)\) is a common factor. Factor \(5x + 4\) out: \[ (5x + 4)(x^2 + 7) \] Thus, the factored form of the polynomial is: \[ (5x + 4)(x^2 + 7) \]