Factor completely -6x2 + 18x – 24. I keep getting the wrong answer :/. Someone please walk me through it? I'll give a medal!

Question

imstuck · Answer

I can help!

imstuck · Answer

Start by factoring out a -6, because -6 goes into all those coefficients.  Like this...

imstuck · Answer

$$-6(x ^{2}-3x+4)$$

imstuck · Answer

Chances are what's inside the parenthesis will also factor now...let's see!

imstuck · Answer

Your set up is like this -6(x - )(x - ).  Are you familiar with this?

anonymous · Answer

Yes I am. But this is the part where I keep getting stuck. Then shouldn't there be factors of something to add up to one of the terms?

imstuck · Answer

Yes, and I did it all sorts of ways, and what's inside the parenthesis does not factor any further.  Let me try the whole thing using the quadratic formula just to make sure I'm correct in saying that doesn't factor into integers, okk?  Give me a sec...

imstuck · Answer

Ok, when you factor that you get this for a solution:

imstuck · Answer

$$\frac{ 3\pm i \sqrt{252} }{ 2 }$$which means that it is an imaginary nonreal set of numbers for the solutions.  So when you take out the -6, that is all you can do...unless you're working with imaginary numbers now in class?

anonymous · Answer

No we're just factoring. But thank you soosososooo much! I just didn't know you couldn't factor further.

imstuck · Answer

You're welcome!!

unklerhaukus · Answer

$$-6x^2 + 18x – 24\
=-6(x^2-3x+4)$$can be factored a little further 
$$=-6\big((x-3)x+4\big)$$