Solved example of algebraic fractions

Let's divide the polynomial by $x+1$ using synthetic division (also known as Ruffini's rule). First, write all the coefficients of the polynomial in the numerator in descending order based on grade (putting a zero if a term doesn't exist). Then, take the first coefficient ($1$) and multiply it by the root of the denominator ($-1$). Add the result to the second coefficient and multiply this by $-1$ and so on

In the last row appear the new coefficients of the polynomial. Use these coefficients to rewrite the new polynomial with a lower grade, and the remainder ($3$) divided by the divisor