There is absolutely no doubt that Jesus Christ never sinned. But, some have wondered if He could He have sinned. After all, He was a normal (see What Did Jesus Look Like?) flesh and blood human - the gory brutality inflicted upon Him at His crucifixion is undeniable proof of that (see The Fateful Night and How Did Jesus Christ Die?).
The verses in the opening paragraph, while stating clearly that Jesus never sinned, also say that He can "sympathize with our weaknesses" and "in every respect has been tempted as we are." Can someone be tempted to do something that's impossible for them to do? For example, can you be tempted to spend the $10.00 in your pocket if you don't have $10.00 in your pocket?
The "temptation of Christ" was not a farce - it was for real. Satan didn't try to get Jesus to sin because he knew that it wasn't possible, but because he knew that it was possible. The Messiah was tempted, truly tempted, but did not sin. He did for us what we cannot do for ourselves (see Blame It On Adam and Eve).
Go Ahead, Jump!
"Then Jesus was led up by the Spirit into the wilderness to be tempted by the devil. And He fasted forty days and forty nights, and afterward He was hungry. And the tempter [see That Old Serpent] came and said to Him, "If you are the Son of God, command these stones to become loaves of bread."
"But He answered, "It is written, 'Man shall not live by bread alone, but by every word that proceeds from the mouth of God.'"
"Then the devil took Him to the holy city, and set Him on the pinnacle of the Temple, and said to Him, "If you are the Son of God, throw yourself down; for it is written, 'He will give His angels charge of you,' and 'On their hands they will bear you up, lest you strike your foot against a stone.'"
"Jesus said to him, "Again it is written, 'You shall not tempt The Lord your God.'"
"Again, the devil took Him to a very high mountain, and showed Him all the kingdoms of the world and the glory of them; and he said to Him, "All these I will give you, if you will fall down and worship me." [see Did God Create The Devil? and The Lame Duck]
"Then Jesus said to him, "Begone, Satan! for it is written, 'You shall worship The Lord your God and Him only shall you serve.'"
"Then the devil left Him, and behold, angels came and ministered to Him." (Matthew 4:1-11 RSV)
Fact Finder: During the "temptation of Christ," did Satan, in an attempt to misuse them for his own evil purposes, actually quote verses from the Psalms to Jesus Christ?
Matthew 4:6, Psalm 91:11-12
See What Does Satan Look Like?