Question

Explain in your own words how you approach solving any quadratic equation by factoring. What are the key things you keep in mind as you’re working towards finding the answer(s)? Your explanation must be at least a few sentences long. Remember to outline your specific, step-by-step process.

Answer 1

Given a quadratic equation , we need to find out two numbers such that

[Caution: These two numbers need not be real numbers always].

Once we find these two numbers, we rewrite the equation as:

.

For the process of factoring we need to write the equation with simplification as:

.

Niw taking x common from the first two terms and common from the last two terms, we get:

.

Finally, taking common, we get:

.

Once we write like that, we get as the solution of the equation.

Example: For the equation, , we need to find two numbers, whose sum is -5 and whose product is 6. We see that these numbers are . Thus [there is no problem in changing the].

Now we may write as:

So, are the solution.