Volume function and Mahler measure of exact polynomials

We study a class of two-variable polynomials called exact which contains $A$ -polynomials knot complements. The Mahler measure these can be computed in terms volume function defined on the vanishing set polynomial. prove that local extrema are two-dimensional torus and give closed formula for extremal values. This shows an irreducible polynomial divided by $\pi$ is greater than amplitude function. also K-theoretic criterion to factor -polynomial topological interpretation its measure.