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

1 Answer
Mar 19, 2018

Answer:

#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!