Yours Truly answers: When we divide  4x² – 5x – 6  by  x – 2  using synthetic division, the correct procedure should look like this:

There are two typical mistakes we sometimes make:

 Common Mistake 1. Use  –2   instead of   2   on the left. This would produce

 In effect, this is the division of  4x² – 5x – 6  by  x + 2, because we must regard  x + 2  as  x + 2 = x – (–2).

 Common Mistake 2. Subtract numbers vertically, instead of adding them. This would produce

 The funny thing is that we ended up with the same wrong answer!

On exams, we can check our answers by multiplying the quotient and the divisor to see if the product comes out to be the same as the original dividend. In the above problem, we check that

The wrong quotient and remainder would not reproduce the original dividend.