So whenever you have a polynomial with powers higher than 2 in it, and you have to solve for when the polynomial = 0, first see if you can simplify it to a quadratic equation, or perhaps an even more simple form.

If not, try guessing values that will make the equation true, and substitute them in to see if they work.  Try simple whole numbers, like 0, 1, 2, 3, 4, then –1, 2, –3, –4.  If none of these guesses work, chances are either the polynomial can be simplified into a simpler form, or the solutions are not ‘nice’ numbers, in which case this method won’t work very well.

Once you have found a number that is a solution, put it into the brackets as shown and conduct the polynomial division. 

If your polynomial division doesn’t nicely come to 0, you have either:

·         used an incorrect guess,

·         made a mistake in your calculations somewhere, or

·         been given an equation which has some nice solutions, but not all nice solutions.