Divide

(x4 + x2 - 80)/(x + 3)


There are two terms missing in the numerator, so we rewrite it as

(x4 + 0x3 + x2 + 0x - 80)/(x + 3)

Then we perform the long division:

            x3 - 3x2 + 10x - 30
x + 3)x4 + 0x3 +  x2 +  0x - 80
      x4 + 3x3
          -3x3 +  x2
          -3x3 - 9x2
                10x2 +  0x
                10x2 + 30x
                      -30x - 80
                      -30x - 90
                             10

Now we write the remainder over the divisor and
add it to the quotient, giving

          x3 - 3x2 + 10x - 30 + 10/(x+3)

Edwin