This section introduces the technique of completing the square.

This section will introduce the technique of completing the square. This is used heavily in certain topics of calculus and trigonometry and isn’t necessarily a type of factoring so much as a technique to manipulate something into a more easily factored form.

Completing the Square

The principle idea of completing the square is to rewrite a quadratic form as a binomial term squared plus/minus a constant. Let’s see an example of what we mean.

In our previous example we were given what the binomial square was at the start but it might not be as obvious what you should choose as your target perfect square just by looking at your polynomial. Luckily there is a way to determine what the target perfect square should be based on your polynomial.

Ok, the above is a bit of alphabet soup, so it will help to see another concrete example following these steps.