We can do this two ways: polynomial division or synthetic division.
Polynomial division involves factoring the equations first. Synthetic division is basically long division.
I'm opting for polynomial division cause it's shorter.
First, we factor ((x^4)-(x^3)-(7x^2)+4x-3).
((x^4)-(x^3)-(7x^2)+4x-3)=(x-3)((x^3)+(2x^2)-x+1)
Then divide:
((x-3)((x^3)+(2x^2)-x+1)) ÷ (x-3) = (x^3)+(2x^2)-x+1
So your answer is B
