We present here the measurement of the single-polymer entropic elasticity and the single covalent bond force profile, probed with two types of atomic force microscopes (AFM) on a synthetic polymer molecule: polymethacrylic acid in water. The conventional AFM allowed us to distinguish two types of interactions present in this system when doing force spectroscopic measurements: the first interaction is associated with adsorption sites of the polymer chains onto a bare gold surface, the second interaction is directly correlated to the rupture process of a single covalent bond. All these bridging interactions allowed us to stretch the single polymer chain and to determine the various factors playing a role in the elasticity of these molecules. To obtain a closer insight into the bond rupture process, we moved to a force sensor stable in position when measuring attractive forces. By optimizing the polymer length so as to fulfill the elastic stability conditions, we were able for the first time to map out the entire force profile associated with the cleavage of a single covalent bond. Experimental data coupled with molecular quantum mechanical calculations strongly suggest that the breaking bond is located at one end of the polymer chain.