All skills learned lead eventually to the ability to solve equations and simplify the solutions.
In previous chapters we have solved equations of the first degree.
We can never multiply two numbers and obtain an answer of zero unless at least one of the numbers is zero.
Of course, both of the numbers can be zero since (0)(0) = 0. The solutions can be indicated either by writing x = 6 and x = - 1 or by using set notation and writing , which we read "the solution set for x is 6 and - 1." In this text we will use set notation.
The general form is (a b) The -7 term immediately says this cannot be a perfect square trinomial.
The task in completing the square is to find a number to replace the -7 such that there will be a perfect square.
This can never be true in the real number system and, therefore, we have no real solution.
Upon completing this section you should be able to: From your experience in factoring you already realize that not all polynomials are factorable.
This method cannot always be used, because not all polynomials are factorable, but it is used whenever factoring is possible.
The method of solving by factoring is based on a simple theorem. We will not attempt to prove this theorem but note carefully what it states.