Use synthetic division to divide 5-3x+4x²-x³/x+1

Answer 1

Put in "standard" order, with highest degree first.

(-x³+4x²-3x+5)/(x+1)

Put the zero of the factor in the denominator in "the box", and write out only the coefficients (the numbers multiplied by the different powers of x)

-1 | -1 4 -3 5

Bring down the first number, then multiply with the number in the box. Add the result to the 2nd number. Multiply sum with number in the box, add result to 3rd number...

-1 | -1 4 -3 5

1 -5 8

.... -1 5 -8 13

Final answer is -x² + 5x - 8 + 13/(x+1)