Factoring polynomials
Factoring polynomials is done in pretty much the similar manner. We determine all of the terms which were multiplied together to obtain the given polynomial. Then we try to factor each of the terms we found in the first step. This continues till we just can't factor anymore.
Completely factored polynomial
While we can't do any more factoring we will say that the polynomial is completely factored.
Here are some examples.
x^{2} -16 = ( x + 4) ( x - 4)
It is completely factored as neither of the two factors on the right can be factored further.
Similarly
x^{4} -16 = ( x^{2} + 4)( x^{2} - 4)
is not completely factored as the second factor can be factored further. Notice that the first factor is completely factored. Here is the complete factorization of this polynomial.
x^{4} -16 = ( x^{2} + 4)( x + 2)( x - 2)
The reason of this section is to familiarize ourselves along several techniques for factoring polynomials.