Question

Divide these polynomials.

(x4 - x3 - 7x2 + 4x - 3) (x - 3)

A. x3 - 3x2 + 2x + 2
B. x3 + 2x2 - x + 1
C. x3 - 2x2 - x + 1
D. x4 + 2x3 - x2 + x

Answer 1

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