Solving Quadratic Equations by Factoring - Problem 4
Here I have a problem that I want to solve by factoring and there’s a couple of things that are making me nervous. The first thing is that it's not in standard form and the second thing is I have a whole bunch of big coefficients. So I’m hoping there might be a greatest common factor.
Let’s start by writing this guy equal to 0 by subtracting 27 from both sides. This stuff stays the same, then I have -27 is equal to 0. Now I’m going to look for a greatest common factor. Greatest common factor meaning a combination of numbers and letters that multiplies into to all three of these terms.
Well you guys can probably tell that 3 goes into all of these I could either factor out 3 or -3. I’m going to factor out -3 just being really careful with the minus signs. If I factor out -3 like un-distributing I’ll have -3 times +6x and times +9 equal to 0.
Now I’m not done factoring yet because this trinomial can be factored even further. -3 times (x plus 3), (x plus 3).
My last step is to use the last product properly but this is one is kind of tricky because I have three things being multiplied together that give me the answer 0. So I could kind of write -3 equal 0 and x plus 3 equals 0 and x plus 3 equals 0, although this is never true right? That means I’m not going to get a solution out of there you don’t even need t worry about the greatest common factor it doesn’t affect my x solutions.
Once I’ve gotten rid of that guy I also notice that the same binomial shows up twice. This is a perfect square trinomial, so that tells me I’m only going to have one answer that answer is going to be x equals -3. The only value that makes this statement true is the value -3. To check you would go back and substitute -3 in here for both Xs and make sure that your answer does indeed give you +27.
When you are doing these problems look for a greatest common factor like this and if it’s just a constant like -3, it’s not going to give you any solution you can just kind of cancel that guy out it doesn’t affect your final solutions here.