The forgotten topological index is defined as the sum of cubes of the degrees of the vertices of the molecular graph $G.$ In this paper, we obtain, analyze, and compare various lower bounds for the forgotten topological index involving the number of vertices, edges, and maximum and minimum vertex degree. Then we give Nordhaus--Gaddum-type inequalities for the forgotten topological index and coindex. Finally, we correct the number of extremal chemical trees on 15 vertices.