Movies like The Da Vinci Code and The Last Temptation of Christ imply Jesus could've sinned. Of course, the faithful know Christ was "without sin," as Hebrews 4:15 attests. But was the God-man able to sin, if He'd wanted to?
The twofold answer is, first, no, Christ, Who is God, could not sin without contradicting His own divine nature; and, second, the deified humanity of Christ could never be torn from God's illuminating embrace.
The Second Person of the Holy Trinity couldn't sin any more than God the Father or God the Holy Spirit could. It's an inherent contradiction to say, with 1 John 4:8, that "God is love," and then claim Divine Love acted without love by sinning.
Nor could Christ, in His human nature, commit sin, as the eternal Christ remained a single divine Person while clothing Himself with human nature. The eternal Son of God became the Son of Mary without becoming two persons, one incapable of sinning and the other able to sin. Splitting Christ into two persons is actually a fifth-century heresy called Nestorianism.
Moreover, Christ's humanity was unable to be an instrument of sin, as the go-to theologian for Catholic seminarians, Fr. Ludwig Ott, explains on page 169 of his theological manual Fundamentals of Catholic Dogma: "From the Hypostatic Union, there arises a physical impossibility of sinning, and the Beatific Vision, a moral impossibility; that is, it involves such a close connection with God in knowledge and love that a turning away from God is actually excluded."
Not only was Christ's humanity perfectly sanctified via the Hypostatic Union, but His human mind was always enlightened by the Beatific Vision, even from Mary's womb, as Pope Pius XII, in Mystici Corporis Christi, affirms: "For hardly was He conceived in the womb of the Mother of God when He began to enjoy the Beatific Vision, and, in that vision, all the members of His Mystical Body were continually and unceasingly present to Him, and He embraced them with His redeeming love."
Explore this mysterious hallmark of Christianity in season one of Armor of God—The Incarnation.