Sketch the function (x^4 + 2x^3 - x -2)/(x+2)

First of all determine the range of the function by looking at its denominator. The function is defined at each point except x=-2 Now to find the zeros of the function first factorise it and equate it to zero y=[( x³-1)(x+2)]/(x+2)=0 and notice how we can get rid of the denominator. Thus the only zero is at x=1. Now we realised that for every x different from -2 the function behaves exactly like (x³-1) which we sketch like a positive cubic shifted of 1 unit downwards. Leaving -2 hollow we conclude the sketch.