Answer
$f(x)=(x-1)(-5x^3-4x^2-2x+1)+2$
Work Step by Step
Step 1. Use the given coefficients to set up the division as shown in the figure.
Step 2. Perform the synthetic division.
Step 3. The answer is $-5x^3-4x^2-2x+1+\frac{2}{x-1}$, thus $f(x)=(x-1)(-5x^3-4x^2-2x+1)+2$