Question: Factor by grouping. 5w^3 + 7w^2 + 25w + 35

Solution

Factor the expression by grouping: The expression is: \[ 5w^3 + 7w^2 + 25w + 35 \] First, group the terms: \[ (5w^3 + 7w^2) + (25w + 35) \] Factor out the greatest common factor in each group: \[ w^2(5w + 7) + 5(5w + 7) \] Notice that \(5w + 7\) is the common factor. So, factor it out: \[ (w^2 + 5)(5w + 7) \] The factored form of the expression is: \[ (w^2 + 5)(5w + 7) \]