Factor the following polynomial by grouping. If it cannot be factored, indicate "Not Factorable".
\[
6 a c-3 b d+b c-18 a d
\]
Answer
So, the factored form of the given polynomial is \(\boxed{(c - 3d)(6a + b)}\).
Step 1 ：First, we rearrange the terms to group them in a way that makes factoring easier. We get: \(6ac - 18ad + bc - 3bd\).
Step 2 ：Next, we factor out the common factors from each group. From the first group, we can factor out \(6a\), and from the second group, we can factor out \(b\). This gives us: \(6a(c - 3d) + b(c - 3d)\).
Step 3 ：Finally, we notice that \((c - 3d)\) is a common factor in both terms. We can factor this out to get our final factored form: \((c - 3d)(6a + b)\).
Step 4 ：So, the factored form of the given polynomial is \(\boxed{(c - 3d)(6a + b)}\).
