There is a general method for finding roots of a cubic, but using it is quite cumbersome. We'll tackle a simplified version of the method here. For convenience sake, we'll abbreviate this to Comparing coefficients gives We'll use these formulas to guess the first root. We need three numbers whose sum is 6 and whose product is also 6. If the higher order polynomial does not divide evenly, a remainder will be left which can be expressed as a fraction.
Some people do synthetic division with the coefficients only and leave out the powers of x.
The reader might want at this point to write down several combinations of numbers that fit. This exercise is valuable for developing guessing ability, which often comes down to brainstorming possible solutions, then quickly evaluating each choice. As above, we'll pick one of the solutions and do a synthetic division to see if it divides the cubic evenly. So our guesses turned out to be correct. Since the answer is known in advance, this exercise is not quite as good as starting from a totally new and unknown cubic, but the point is that the reader can make and then do many examples.