SOLUTION: write an equation in standard form that you can solve by factoring and one that you cannot solve by factoring.

Question 231639: write an equation in standard form that you can solve by factoring and one that you cannot solve by factoring.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I'm going to go way out on a limb and presume that you mean a quadratic equation.

In fact, there is no such thing as a quadratic equation that cannot be solved by factoring. Even if you have irrational or complex roots, you still have roots. And if you have roots, you have factors. Now, in many cases it may be very difficult to find the factors and you may have to resort to other means to solve the equation.

For example, consider:

which does not factor over the integers (doesn't factor over the rationals, either). The quadratic formula tells us that the roots are:

Meaning that:

Deucedly difficult to solve by factoring, but not entirely impossible.

On the other hand, if you did not ask the ENTIRE question, that is, if the question was "...cannot solve by factoring over the real numbers (or rationals, or integers)" then you could give:

: No real number factors

as an example for the second half of your question.

John

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