To factor the given expression using the factor by grouping technique, follow these steps:
Step 1: Look for the common factors, if any. In this case, there are no common factors among the terms.
Step 2: Group the terms. Rearrange the expression by grouping the terms as follows:
(30x^3 + 18x^2) + (-5x - 3)
Step 3: Factor out the common factor from each group.
For the first group (30x^3 + 18x^2), we can factor out 6x^2, resulting in:
6x^2(5x + 3).
For the second group (-5x - 3), we can factor out -1, resulting in:
-1(5x + 3).
Step 4: Check if there are any common factors left. In this case, we can see that both groups have a common factor of (5x + 3).
Step 5: Combine the common factors. The final factored form is:
(5x + 3)(6x^2 - 1).
So, the factored form of the given expression 30x^3 + 18x^2 - 5x - 3 using the factor by grouping technique is (5x + 3)(6x^2 - 1).