Factor by grouping. \[ 8 c^{2}+38 c+35 \]

Step 1 ：Group the terms in pairs: (8c^2 + 38c) + 35.

Step 2 ：Factor out the greatest common factor (GCF) from each group. The GCF of the first group is 2c, and the GCF of the second group is 35.

Step 3 ：After factoring out the GCF, we should have two terms that are the same. If they are not the same, then the expression cannot be factored by grouping.

Step 4 ：The factored form of the expression \(8 c^{2}+38 c+35\) is \(\boxed{(2c + 7)(4c + 5)}\).