In "Biblical Perspective" Gordon Snider writes:

The perfect obedience of Christ is a standard that no man on his own can equal. When man compares himself with Christ, he sees how totally impossible it is for him to “establish [his] own righteousness.” Christ did not destroy the law, but His perfect obedience made it forever impossible for man to claim his own righteousness as a reason for salvation. But notice the qualification — to every one that believeth. Once a man believes in Christ as Savior, he abandons any attempt to attain righteousness by his own merit. For those without faith, Christ is not the end of the law for righteousness. They, like the Jews of verse 3, continue the vain effort of salvation by works.

Source: Studies in Romans: Adult Teacher's Insights, page 59.

In "God's Word for Today" William Snider writes:

Paul's emphasis on the redeeming work of Christ flows out of his intense burden for the Jewish people. Reflecting upon his own background as a Pharisee, he could appreciate that they were zealous for what they understood to be God's purpose and method, but they had misunderstood and twisted the plan to emphasize the human rather than the divine. Their insistence upon the obedience to the law had, in fact, revealed their impotence to keep the law. Yet they had wrapped themselves in self-righteous robes and pronounced themselves acceptable to God. The result was an ethical (and racial) arrogance. The true salvation process is to admit sin and come to Jesus for divine forgiveness. It is a purposeful acknowledgment of Christ as the sole source of salvation and faith in His death to accomplish this purpose. For the Jew, this was to reject their system of religion which had major implications for past and present. Accepting Christ for salvation is no less radical now.

Source: Studies in Romans: Adult Teacher's Insights, page 58-59.