Question

How do you solve `3x^2-27=0` by factoring?

Answer 1

`x=+-3`

Explanation:

We can factor out a `3` from both terms. Here, we are essentially dividing. We get:

`3color(blue)((x^2-9))=0`

What I have in blue is called a Difference of Squares. What this means is that if I have the binomial

`a^2-b^2`

Then it can be factored as `(a+b)(a-b)`

In our example, `a` would be `x` (square root of `x^2`) and `b` would be `3` (square root of `9`).

Since `a=x` and `b=3`, we have

`3underbrace((x+3)(x-3))_(x^2-9)=0`

Setting each factor equal to zero, we get:

`x=3` and `x=-3`, or alternatively, `x=+-3`

If the concept of a "Difference of Squares" seems foreign to you, I encourage you to Google it or search it on Khan Academy to make sure you understand it.

Hope this helps!