What must be added to 3x-7 to make x^24x-1

You need to add:  x2+x+6

Let the unknown part be represented by A

Then we have:  3x−7+A=x2+4x−1

Subtract 3x from both sides

−7+A=x2+4x−3x−1

but 4x−3x is giving:

−7+A=x2+x−1

Add 7 to both sides

A=x2+x+6

So you need to add: x2+x+6